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Diagonals of self-adjoint operators I: Compact operators
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-03-18 DOI: 10.1016/j.jfa.2025.110939
Marcin Bownik , John Jasper
{"title":"Diagonals of self-adjoint operators I: Compact operators","authors":"Marcin Bownik ,&nbsp;John Jasper","doi":"10.1016/j.jfa.2025.110939","DOIUrl":"10.1016/j.jfa.2025.110939","url":null,"abstract":"<div><div>Given a self-adjoint operator <em>T</em> on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set <span><math><mi>D</mi><mo>(</mo><mi>T</mi><mo>)</mo></math></span> of all possible diagonals of <em>T</em>. For compact operators <em>T</em>, we give a complete characterization of diagonals modulo the kernel of <em>T</em>. That is, we characterize <span><math><mi>D</mi><mo>(</mo><mi>T</mi><mo>)</mo></math></span> for the class of operators sharing the same nonzero eigenvalues (with multiplicities) as <em>T</em>. Moreover, we determine <span><math><mi>D</mi><mo>(</mo><mi>T</mi><mo>)</mo></math></span> for a fixed compact operator <em>T</em>, modulo the kernel problem for positive compact operators with finite-dimensional kernel.</div><div>Our results generalize a characterization of diagonals of trace class positive operators by Arveson and Kadison <span><span>[5]</span></span> and diagonals of compact positive operators by Kaftal and Weiss <span><span>[24]</span></span> and Loreaux and Weiss <span><span>[28]</span></span>. The proof uses the technique of diagonal-to-diagonal results, which was pioneered in the earlier joint work of the authors with Siudeja <span><span>[12]</span></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 5","pages":"Article 110939"},"PeriodicalIF":1.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738470","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}
引用次数: 0
Murray–von Neumann dimension for strictly semifinite weights
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-03-18 DOI: 10.1016/j.jfa.2025.110938
Aldo Garcia Guinto, Matthew Lorentz, Brent Nelson
{"title":"Murray–von Neumann dimension for strictly semifinite weights","authors":"Aldo Garcia Guinto,&nbsp;Matthew Lorentz,&nbsp;Brent Nelson","doi":"10.1016/j.jfa.2025.110938","DOIUrl":"10.1016/j.jfa.2025.110938","url":null,"abstract":"<div><div>Given a von Neumann algebra <em>M</em> equipped with a faithful normal strictly semifinite weight <em>φ</em>, we develop a notion of Murray–von Neumann dimension over <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>φ</mi><mo>)</mo></math></span> that is defined for modules over the basic construction associated to the inclusion <span><math><msup><mrow><mi>M</mi></mrow><mrow><mi>φ</mi></mrow></msup><mo>⊂</mo><mi>M</mi></math></span>. For <span><math><mi>φ</mi><mo>=</mo><mi>τ</mi></math></span> a faithful normal tracial state, this recovers the usual Murray–von Neumann dimension for finite von Neumann algebras. If <em>M</em> is either a type <span><math><msub><mrow><mi>III</mi></mrow><mrow><mi>λ</mi></mrow></msub></math></span> factor with <span><math><mn>0</mn><mo>&lt;</mo><mi>λ</mi><mo>&lt;</mo><mn>1</mn></math></span> or a full type <span><math><msub><mrow><mi>III</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> factor with <span><math><mi>Sd</mi><mo>(</mo><mi>M</mi><mo>)</mo><mo>≠</mo><mi>R</mi></math></span>, then amongst extremal almost periodic weights the dimension function depends on <em>φ</em> only up to scaling. As an application, we show that if an inclusion of diffuse factors with separable preduals <span><math><mi>N</mi><mo>⊂</mo><mi>M</mi></math></span> is with expectation <span><math><mi>E</mi></math></span> and admits a compatible extremal almost periodic state <em>φ</em>, then this dimension quantity bounds the index <span><math><mi>Ind</mi><mspace></mspace><mi>E</mi></math></span>, and in fact equals it when the modular operators <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>φ</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>φ</mi><msub><mrow><mo>|</mo></mrow><mrow><mi>N</mi></mrow></msub></mrow></msub></math></span> have the same point spectrum. In the pursuit of this result, we also show such inclusions always admit Pimsner–Popa orthogonal bases.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 5","pages":"Article 110938"},"PeriodicalIF":1.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738469","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}
引用次数: 0
The concept of mapped coercivity for nonlinear operators in Banach spaces
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-03-06 DOI: 10.1016/j.jfa.2025.110893
Roland Becker , Malte Braack
{"title":"The concept of mapped coercivity for nonlinear operators in Banach spaces","authors":"Roland Becker ,&nbsp;Malte Braack","doi":"10.1016/j.jfa.2025.110893","DOIUrl":"10.1016/j.jfa.2025.110893","url":null,"abstract":"<div><div>We provide a concise proof of existence of the solutions to nonlinear operator equations in separable Banach spaces, without assuming the operator to be monotone. Instead, our main hypotheses consist of a continuity assumption and a mapped coercivity property, which is a generalization of the usual coercivity property for nonlinear operators. In the case of linear operators, we recover the traditional inf-sup condition. To illustrate the applicability of this general concept, we apply it to semi-linear elliptic problems and the Navier-Stokes equations.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 3","pages":"Article 110893"},"PeriodicalIF":1.7,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143620534","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}
引用次数: 0
A new characterization of the dissipation structure and the relaxation limit for the compressible Euler-Maxwell system
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-03-05 DOI: 10.1016/j.jfa.2025.110918
Timothée Crin-Barat , Yue-Jun Peng , Ling-Yun Shou , Jiang Xu
{"title":"A new characterization of the dissipation structure and the relaxation limit for the compressible Euler-Maxwell system","authors":"Timothée Crin-Barat ,&nbsp;Yue-Jun Peng ,&nbsp;Ling-Yun Shou ,&nbsp;Jiang Xu","doi":"10.1016/j.jfa.2025.110918","DOIUrl":"10.1016/j.jfa.2025.110918","url":null,"abstract":"<div><div>We investigate the three-dimensional compressible Euler-Maxwell system, a model for simulating the transport of electrons interacting with propagating electromagnetic waves in semiconductor devices. First, we establish the global well-posedness of classical solutions near constant equilibrium in a critical regularity setting, uniformly with respect to the relaxation parameter <span><math><mi>ε</mi><mo>&gt;</mo><mn>0</mn></math></span>. Then, we introduce an effective unknown motivated by Darcy's law to derive quantitative error estimates at the rate <span><math><mi>O</mi><mo>(</mo><mi>ε</mi><mo>)</mo></math></span> between the rescaled Euler-Maxwell system and the limiting drift-diffusion model. This provides the first global-in-time strong convergence result for the relaxation procedure in the case of ill-prepared data so far.</div><div>We propose a new characterization of the dissipation structure for the non-symmetric relaxation of linearized Euler-Maxwell system, which partitions the frequency space into three distinct regimes (low, medium and high frequencies) associated with different behaviors of the solution. Within each regime, the application of Lyapunov functionals based on the hypocoercivity theory reveals the expected dissipative properties. Moreover, two correction functions are employed to take care of the initial layers in the relaxation convergence.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 2","pages":"Article 110918"},"PeriodicalIF":1.7,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143601522","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}
引用次数: 0
Convergences of combinatorial Ricci flows to degenerated circle packings in hyperbolic background geometry
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-03-05 DOI: 10.1016/j.jfa.2025.110921
Guangming Hu , Sicheng Lu , Dong Tan , Youliang Zhong , Puchun Zhou
{"title":"Convergences of combinatorial Ricci flows to degenerated circle packings in hyperbolic background geometry","authors":"Guangming Hu ,&nbsp;Sicheng Lu ,&nbsp;Dong Tan ,&nbsp;Youliang Zhong ,&nbsp;Puchun Zhou","doi":"10.1016/j.jfa.2025.110921","DOIUrl":"10.1016/j.jfa.2025.110921","url":null,"abstract":"<div><div>This paper investigates a kind of degenerated circle packings in hyperbolic background geometry. A main problem is whether a prescribed total geodesic curvature data can be realized by a degenerated circle packing or not. We fully characterize the sufficient and necessary conditions and show the uniqueness. Furthermore, we introduce the combinatorial Ricci flow to find the desired degenerated circle packed surface, analogous to the methods of Chow-Luo <span><span>[7]</span></span> and Takatsu <span><span>[37]</span></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 3","pages":"Article 110921"},"PeriodicalIF":1.7,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143620533","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}
引用次数: 0
A bridge connecting convex analysis and complex analysis and L2-estimate of d and ∂¯
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-03-05 DOI: 10.1016/j.jfa.2025.110917
Fusheng Deng , Jinjin Hu , Weiwen Jiang , Xiangsen Qin
{"title":"A bridge connecting convex analysis and complex analysis and L2-estimate of d and ∂¯","authors":"Fusheng Deng ,&nbsp;Jinjin Hu ,&nbsp;Weiwen Jiang ,&nbsp;Xiangsen Qin","doi":"10.1016/j.jfa.2025.110917","DOIUrl":"10.1016/j.jfa.2025.110917","url":null,"abstract":"<div><div>We propose a way to connect complex analysis and convex analysis. As applications, we derive some results about <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-estimate for <em>d</em>-equation and prove some curvature positivity related to convex analysis from well known <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-estimate for <span><math><mover><mrow><mo>∂</mo></mrow><mrow><mo>¯</mo></mrow></mover></math></span>-equation or the results we prove in complex analysis.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 2","pages":"Article 110917"},"PeriodicalIF":1.7,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143579174","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}
引用次数: 0
Increasing resolution and instability for linear inverse scattering problems
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-03-05 DOI: 10.1016/j.jfa.2025.110923
Pu-Zhao Kow , Mikko Salo , Sen Zou
{"title":"Increasing resolution and instability for linear inverse scattering problems","authors":"Pu-Zhao Kow ,&nbsp;Mikko Salo ,&nbsp;Sen Zou","doi":"10.1016/j.jfa.2025.110923","DOIUrl":"10.1016/j.jfa.2025.110923","url":null,"abstract":"<div><div>In this work we study the increasing resolution of linear inverse scattering problems at a large fixed frequency. We consider the problem of recovering the density of a Herglotz wave function, and the linearized inverse scattering problem for a potential. It is shown that the number of features that can be stably recovered (stable region) becomes larger as the frequency increases, whereas one has strong instability for the rest of the features (unstable region). To show this rigorously, we prove that the singular values of the forward operator stay roughly constant in the stable region and decay exponentially in the unstable region. The arguments are based on structural properties of the problems and they involve the Courant min-max principle for singular values, quantitative Agmon-Hörmander estimates, and a Schwartz kernel computation based on the coarea formula.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 1","pages":"Article 110923"},"PeriodicalIF":1.7,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143611576","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}
引用次数: 0
Extremes of interpolation scales of Banach spaces
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-03-05 DOI: 10.1016/j.jfa.2025.110924
Willian Corrêa , Valentin Ferenczi , Rafaela Gesing , Pedro Tradacete
{"title":"Extremes of interpolation scales of Banach spaces","authors":"Willian Corrêa ,&nbsp;Valentin Ferenczi ,&nbsp;Rafaela Gesing ,&nbsp;Pedro Tradacete","doi":"10.1016/j.jfa.2025.110924","DOIUrl":"10.1016/j.jfa.2025.110924","url":null,"abstract":"<div><div>M. Daher gave conditions so that the spheres of the spaces in the interior of a complex interpolation scale are uniformly homeomorphic. We look for sufficient conditions for the validity of this result and related ones on the extremes of the scale, with applications to uniform homeomorphism between spheres of Banach spaces and the sphere of the Hilbert space.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 2","pages":"Article 110924"},"PeriodicalIF":1.7,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143636874","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}
引用次数: 0
Ricci-DeTurck flow from rough metrics and applications to scalar curvature problems
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-03-05 DOI: 10.1016/j.jfa.2025.110916
Jianchun Chu , Man-Chun Lee
{"title":"Ricci-DeTurck flow from rough metrics and applications to scalar curvature problems","authors":"Jianchun Chu ,&nbsp;Man-Chun Lee","doi":"10.1016/j.jfa.2025.110916","DOIUrl":"10.1016/j.jfa.2025.110916","url":null,"abstract":"<div><div>Motivated by the recent work of Lamm and Simon, in this work we study the short-time existence theory of Ricci-DeTurck flow starting from rough metrics which are bi-Lipschitz and have small local scaling invariant gradient concentration. As applications, we use the Ricci flow smoothing to show that scalar curvature lower bound is preserved under bi-Lipschitz <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>n</mi></mrow></msup></math></span> convergence. This is an counter-part of the celebrated work of Gromov and Bamler. We also use similar idea to study stability problems in scalar curvature geometry.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 2","pages":"Article 110916"},"PeriodicalIF":1.7,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143578525","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}
引用次数: 0
Geometric interpretation of the vanishing Lie Bracket for two-dimensional rough vector fields
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-03-04 DOI: 10.1016/j.jfa.2025.110919
Rebucci A., Zizza M.
{"title":"Geometric interpretation of the vanishing Lie Bracket for two-dimensional rough vector fields","authors":"Rebucci A.,&nbsp;Zizza M.","doi":"10.1016/j.jfa.2025.110919","DOIUrl":"10.1016/j.jfa.2025.110919","url":null,"abstract":"<div><div>In this paper, we prove that if <span><math><mi>X</mi><mo>,</mo><mi>Y</mi></math></span> are continuous, Sobolev vector fields with bounded divergence on the real plane and <span><math><mo>[</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>]</mo><mo>=</mo><mn>0</mn></math></span>, then their flows commute. In particular, we improve the previous result of <span><span>[13]</span></span>, where the authors require the additional assumption of the weak Lie differentiability on one of the two flows. We also discuss possible extensions to the BV setting.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 1","pages":"Article 110919"},"PeriodicalIF":1.7,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143576837","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}
引用次数: 0
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