Journal of Functional Analysis最新文献

{"title":"On the weak⁎ separability of the space of Lipschitz functions","authors":"Leandro Candido ,&nbsp;Marek Cúth ,&nbsp;Benjamin Vejnar","doi":"10.1016/j.jfa.2025.110925","DOIUrl":"10.1016/j.jfa.2025.110925","url":null,"abstract":"<div><div>We conjecture that whenever <em>M</em> is a metric space of density at most continuum, then the space of Lipschitz functions is <span><math><msup><mrow><mi>w</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-separable. We prove the conjecture for several classes of metric spaces including all the Banach spaces with a projectional skeleton, Banach spaces with a <span><math><msup><mrow><mi>w</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-separable dual unit ball and locally separable complete metric spaces.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 1","pages":"Article 110925"},"PeriodicalIF":1.7,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143562743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analytic semigroups approaching a Schrödinger group on real foliated metric manifolds","authors":"Rudrajit Banerjee ,&nbsp;Max Niedermaier","doi":"10.1016/j.jfa.2025.110898","DOIUrl":"10.1016/j.jfa.2025.110898","url":null,"abstract":"<div><div>On real metric manifolds admitting a co-dimension one foliation, sectorial operators are introduced that interpolate between the generalized Laplacian and the d'Alembertian. This is used to construct a one-parameter family of analytic semigroups that remains well-defined into the near Lorentzian regime. In the strict Lorentzian limit we identify a sense in which a well-defined Schrödinger evolution group arises. For the analytic semigroups we show in addition that: (i) they act as integral operators with kernels that are jointly smooth in the semigroup time and both spacetime arguments. (ii) the diagonal of the kernels admits an asymptotic expansion in (shifted) powers of the semigroup time whose coefficients are the Seeley-deWitt coefficients evaluated on the complex metrics.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 1","pages":"Article 110898"},"PeriodicalIF":1.7,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143576850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The transition to instability for stable shear flows in inviscid fluids","authors":"Daniel Sinambela,&nbsp;Weiren Zhao","doi":"10.1016/j.jfa.2025.110905","DOIUrl":"10.1016/j.jfa.2025.110905","url":null,"abstract":"<div><div>In this paper, we study the generation of eigenvalues of a stable monotonic shear flow under perturbations in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>s</mi></mrow></msup></math></span> with <span><math><mi>s</mi><mo>&lt;</mo><mn>2</mn></math></span>. More precisely, we study the Rayleigh operator <span><math><msub><mrow><mi>L</mi></mrow><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>γ</mi></mrow></msub></mrow></msub><mo>=</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>γ</mi></mrow></msub><msub><mrow><mo>∂</mo></mrow><mrow><mi>x</mi></mrow></msub><mo>−</mo><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>γ</mi></mrow><mrow><mo>″</mo></mrow></msubsup><msub><mrow><mo>∂</mo></mrow><mrow><mi>x</mi></mrow></msub><msup><mrow><mi>Δ</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span> associated with perturbed shear flow <span><math><mo>(</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>γ</mi></mrow></msub><mo>(</mo><mi>y</mi><mo>)</mo><mo>,</mo><mn>0</mn><mo>)</mo></math></span> in a finite channel <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>2</mn><mi>π</mi></mrow></msub><mo>×</mo><mo>[</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> where <span><math><msub><mrow><mi>U</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>γ</mi></mrow></msub><mo>(</mo><mi>y</mi><mo>)</mo><mo>=</mo><mi>U</mi><mo>(</mo><mi>y</mi><mo>)</mo><mo>+</mo><mi>m</mi><msup><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow></msup><mover><mrow><mi>Γ</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><mi>y</mi><mo>/</mo><mi>γ</mi><mo>)</mo></math></span> with <span><math><mi>U</mi><mo>(</mo><mi>y</mi><mo>)</mo></math></span> being a stable monotonic shear flow and <span><math><msub><mrow><mo>{</mo><mi>m</mi><msup><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow></msup><mover><mrow><mi>Γ</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><mi>y</mi><mo>/</mo><mi>γ</mi><mo>)</mo><mo>}</mo></mrow><mrow><mi>m</mi><mo>≥</mo><mn>0</mn></mrow></msub></math></span> being a family of perturbations parameterized by <em>m</em>. We prove that there exists <span><math><msub><mrow><mi>m</mi></mrow><mrow><mo>⁎</mo></mrow></msub></math></span> such that for <span><math><mn>0</mn><mo>≤</mo><mi>m</mi><mo>&lt;</mo><msub><mrow><mi>m</mi></mrow><mrow><mo>⁎</mo></mrow></msub></math></span>, the Rayleigh operator has no eigenvalue or embedded eigenvalue, therefore linear inviscid damping holds. Otherwise, instability occurs when <span><math><mi>m</mi><mo>≥</mo><msub><mrow><mi>m</mi></mrow><mrow><mo>⁎</mo></mrow></msub></math></span>. Moreover, at the nonlinear level, we show that asymptotic instability holds for <em>m</em> near <span><math><msub><mrow><mi>m</mi></mrow><mrow><mo>⁎</mo></mrow></msub></math></span> and growing modes exist for <span><math><mi>m</mi><mo>&gt;</mo><msub><mrow><mi>m</mi></mrow><mrow><mo>⁎</mo></mrow></msub></math></span> which equivalently leads to instability.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 2","pages":"Article 110905"},"PeriodicalIF":1.7,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143578528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Characterizations of the Crandall–Pazy class of C0-semigroups on Hilbert spaces and their application to decay estimates","authors":"Masashi Wakaiki","doi":"10.1016/j.jfa.2025.110902","DOIUrl":"10.1016/j.jfa.2025.110902","url":null,"abstract":"<div><div>We investigate immediately differentiable <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-semigroups <span><math><msub><mrow><mo>(</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>t</mi><mi>A</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>t</mi><mo>≥</mo><mn>0</mn></mrow></msub></math></span> satisfying <span><math><msub><mrow><mi>sup</mi></mrow><mrow><mn>0</mn><mo>&lt;</mo><mi>t</mi><mo>&lt;</mo><mn>1</mn></mrow></msub><mo>⁡</mo><msup><mrow><mi>t</mi></mrow><mrow><mn>1</mn><mo>/</mo><mi>β</mi></mrow></msup><mo>‖</mo><mi>A</mi><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>t</mi><mi>A</mi></mrow></msup><mo>‖</mo><mo>&lt;</mo><mo>∞</mo></math></span> for some <span><math><mn>0</mn><mo>&lt;</mo><mi>β</mi><mo>≤</mo><mn>1</mn></math></span>. Such <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-semigroups are referred to as the Crandall–Pazy class of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-semigroups. In the Hilbert space setting, we present two characterizations of the Crandall–Pazy class. We then apply these characterizations to estimate decay rates for Crank–Nicolson schemes with smooth initial data when the associated abstract Cauchy problem is governed by an exponentially stable <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-semigroup in the Crandall–Pazy class. The first approach is based on a functional calculus called the <span><math><mi>B</mi></math></span>-calculus. The second approach builds upon estimates derived from Lyapunov equations and improves the decay estimate obtained in the first approach, under the additional assumption that <span><math><mo>−</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span> generates a bounded <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-semigroup.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 3","pages":"Article 110902"},"PeriodicalIF":1.7,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143620535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gap theorems for complete self-shrinkers of r-mean curvature flows","authors":"Hilário Alencar ,&nbsp;G. Pacelli Bessa ,&nbsp;Gregório Silva Neto","doi":"10.1016/j.jfa.2025.110920","DOIUrl":"10.1016/j.jfa.2025.110920","url":null,"abstract":"<div><div>In this paper, we prove gap results for complete self-shrinkers of the <em>r</em>-mean curvature flow involving a modified second fundamental form. These results extend previous results for self-shrinkers of the mean curvature flow due to Cao-Li and Cheng-Peng. To prove our results we show that, under suitable curvature bounds, proper self-shrinkers are parabolic for a certain second-order differential operator which generalizes the drifted Laplacian and, even if is not proper, this differential operator satisfies an Omori-Yau type maximum principle.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 1","pages":"Article 110920"},"PeriodicalIF":1.7,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143576838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An improved dense class in Sobolev spaces to manifolds","authors":"Antoine Detaille","doi":"10.1016/j.jfa.2025.110894","DOIUrl":"10.1016/j.jfa.2025.110894","url":null,"abstract":"<div><div>We consider the strong density problem in the Sobolev space <span><math><msup><mrow><mi>W</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>p</mi></mrow></msup><mo>(</mo><msup><mrow><mi>Q</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>;</mo><mi>N</mi><mo>)</mo></math></span> of maps with values into a compact Riemannian manifold <span><math><mi>N</mi></math></span>. It is known, from the seminal work of Bethuel, that such maps may always be strongly approximated by <span><math><mi>N</mi></math></span>-valued maps that are smooth outside of a finite union of <span><math><mo>(</mo><mi>m</mi><mo>−</mo><mo>⌊</mo><mi>s</mi><mi>p</mi><mo>⌋</mo><mo>−</mo><mn>1</mn><mo>)</mo></math></span>-planes. Our main result establishes the strong density in <span><math><msup><mrow><mi>W</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>p</mi></mrow></msup><mo>(</mo><msup><mrow><mi>Q</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>;</mo><mi>N</mi><mo>)</mo></math></span> of an improved version of the class introduced by Bethuel, where the maps have a singular set <em>without crossings</em>. This answers a question raised by Brezis and Mironescu.</div><div>In the special case where <span><math><mi>N</mi></math></span> has a sufficiently simple topology and for some values of <em>s</em> and <em>p</em>, this result was known to follow from the <em>method of projection</em>, which takes its roots in the work of Federer and Fleming. As a first result, we implement this method in the full range of <em>s</em> and <em>p</em> in which it was expected to be applicable. In the case of a general target manifold, we devise a topological argument that allows to remove the self-intersections in the singular set of the maps obtained via Bethuel's technique.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 2","pages":"Article 110894"},"PeriodicalIF":1.7,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143578530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Volterra operator acting on Bergman spaces of Dirichlet series","authors":"Carlos Gómez-Cabello ,&nbsp;Pascal Lefèvre ,&nbsp;Hervé Queffélec","doi":"10.1016/j.jfa.2025.110906","DOIUrl":"10.1016/j.jfa.2025.110906","url":null,"abstract":"<div><div>Since their introduction in 1997, Hardy spaces of Dirichlet series have been broadly studied. The increasing interest which they sparked motivated the introduction of new such spaces, as the Bergman spaces <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mi>p</mi></mrow></msubsup></math></span> considered here, with <em>μ</em> a probability measure. Similarly, recent lines of research have focused on the study of some classical operators acting on these spaces, like the Volterra operator <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span>. In this work, we introduce a new family of spaces of Dirichlet series, the <span><math><msub><mrow><mtext>Bloch</mtext></mrow><mrow><mi>μ</mi></mrow></msub></math></span>-spaces. We can provide, in terms of those spaces, a sufficient condition for this Volterra operator to act boundedly on the spaces <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mi>p</mi></mrow></msubsup></math></span>. We also establish a necessary condition for a specific choice of <em>μ</em>. Sufficient and necessary conditions for compactness are also proven. The non-membership in Schatten classes is established, as well as a radicality result for some Bloch space.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 3","pages":"Article 110906"},"PeriodicalIF":1.7,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143620537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spectral zeta function and ground state of quantum Rabi model","authors":"Fumio Hiroshima,&nbsp;Tomoyuki Shirai","doi":"10.1016/j.jfa.2025.110901","DOIUrl":"10.1016/j.jfa.2025.110901","url":null,"abstract":"<div><div>The spectral zeta function <span><math><msub><mrow><mi>ζ</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>(</mo><mi>s</mi><mo>;</mo><msup><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>τ</mi><mo>)</mo><mo>=</mo><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mrow><mo>∞</mo></mrow></msubsup><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mo>(</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo><mo>+</mo><msup><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>τ</mi><mo>)</mo></mrow><mrow><mi>s</mi></mrow></msup></mrow></mfrac></math></span> of the quantum Rabi Hamiltonian is considered, where <span><math><mi>τ</mi><mo>&gt;</mo><mn>0</mn></math></span> and <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>g</mi><mo>)</mo></math></span> denotes <em>n</em>th eigenvalue of the quantum Rabi Hamiltonian <em>H</em>. Let <span><math><mi>ζ</mi><mo>(</mo><mi>s</mi><mo>;</mo><mi>τ</mi><mo>)</mo><mo>=</mo><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mrow><mo>∞</mo></mrow></msubsup><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mi>τ</mi><mo>)</mo></mrow><mrow><mi>s</mi></mrow></msup></mrow></mfrac></math></span> be the Hurwitz zeta function. It is shown that <span><math><msub><mrow><mi>lim</mi></mrow><mrow><mo>|</mo><mi>g</mi><mo>|</mo><mo>→</mo><mo>∞</mo></mrow></msub><mo>⁡</mo><msub><mrow><mi>ζ</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>(</mo><mi>s</mi><mo>;</mo><msup><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>τ</mi><mo>)</mo><mo>=</mo><mn>2</mn><mi>ζ</mi><mo>(</mo><mi>s</mi><mo>;</mo><mi>τ</mi><mo>)</mo></math></span>. Moreover the path measure <span><math><msub><mrow><mi>Π</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> associated with the ground state of <em>H</em> is constructed on a discontinuous path space, and several applications are shown.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 3","pages":"Article 110901"},"PeriodicalIF":1.7,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143620536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Almost Auerbach, Markushevich and Schauder bases in Hilbert and Banach spaces","authors":"Anton Tselishchev","doi":"10.1016/j.jfa.2025.110895","DOIUrl":"10.1016/j.jfa.2025.110895","url":null,"abstract":"<div><div>For any sequence of positive numbers <span><math><msubsup><mrow><mo>(</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup></math></span> such that <span><math><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup><msub><mrow><mi>ε</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><mo>∞</mo></math></span> we provide an explicit simple construction of <span><math><mo>(</mo><mn>1</mn><mo>+</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span>-bounded Markushevich basis in a separable Hilbert space which is not strong, or, in other terminology, is not hereditary complete; this condition on the sequence <span><math><msubsup><mrow><mo>(</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup></math></span> is sharp. Using a finite-dimensional version of this construction, Dvoretzky's theorem and a construction of Vershynin, we conclude that in any Banach space for any sequence of positive numbers <span><math><msubsup><mrow><mo>(</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup></math></span> such that <span><math><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup><msubsup><mrow><mi>ε</mi></mrow><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>=</mo><mo>∞</mo></math></span> there exists a <span><math><mo>(</mo><mn>1</mn><mo>+</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span>-bounded Markushevich basis which is not a Schauder basis after any permutation of its elements.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 1","pages":"Article 110895"},"PeriodicalIF":1.7,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The ideal separation property for reduced group C⁎-algebras","authors":"Are Austad ,&nbsp;Hannes Thiel","doi":"10.1016/j.jfa.2025.110904","DOIUrl":"10.1016/j.jfa.2025.110904","url":null,"abstract":"<div><div>We say that an inclusion of an algebra <em>A</em> into a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra <em>B</em> has the ideal separation property if closed ideals in <em>B</em> can be recovered by their intersection with <em>A</em>. Such inclusions have attractive properties from the point of view of harmonic analysis and noncommutative geometry. We establish several permanence properties of locally compact groups for which <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>G</mi><mo>)</mo><mo>⊆</mo><msubsup><mrow><mi>C</mi></mrow><mrow><mi>red</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mi>G</mi><mo>)</mo></math></span> has the ideal separation property.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 1","pages":"Article 110904"},"PeriodicalIF":1.7,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143562741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}