Bulletin of the London Mathematical Society最新文献

{"title":"On the chain of commuting operators on Banach spaces","authors":"Tomasz Szczepanski","doi":"10.1112/blms.70471","DOIUrl":"https://doi.org/10.1112/blms.70471","url":null,"abstract":"<p>An operator <span></span><math>\u0000 <semantics>\u0000 <mi>T</mi>\u0000 <annotation>$T$</annotation>\u0000 </semantics></math> on a Banach space is said to be of chain <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$N$</annotation>\u0000 </semantics></math> if there exist non-scalar operators <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>S</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mi>⋯</mi>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>S</mi>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$S_1,dots,S_{N-1}$</annotation>\u0000 </semantics></math> and a non-zero compact operator <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math> such that\u0000\u0000 </p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 9","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70471","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148784788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Singularity of non-pluripolar cohomology classes","authors":"Duc-Bao Nguyen,&nbsp;Shuang Su,&nbsp;Duc-Viet Vu","doi":"10.1112/blms.70480","DOIUrl":"https://doi.org/10.1112/blms.70480","url":null,"abstract":"<p>We establish a relation between Lelong numbers and the full mass property of relative non-pluripolar products. We use this relation to prove that if the restricted volume of a big class <span></span><math>\u0000 <semantics>\u0000 <mi>α</mi>\u0000 <annotation>$alpha$</annotation>\u0000 </semantics></math> along an effective divisor <span></span><math>\u0000 <semantics>\u0000 <mi>D</mi>\u0000 <annotation>$D$</annotation>\u0000 </semantics></math> has full mass, then the Lelong numbers of the non-pluripolar class <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>⟨</mo>\u0000 <msup>\u0000 <mi>α</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>⟩</mo>\u0000 </mrow>\u0000 <annotation>$langle alpha ^{n-1}rangle$</annotation>\u0000 </semantics></math> at every point in the support of <span></span><math>\u0000 <semantics>\u0000 <mi>D</mi>\u0000 <annotation>$D$</annotation>\u0000 </semantics></math> are zero. In particular, we obtain that on projective manifolds, the Lelong numbers of the non-pluripolar class <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>⟨</mo>\u0000 <msup>\u0000 <mi>α</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>⟩</mo>\u0000 </mrow>\u0000 <annotation>$langle alpha ^{n-1}rangle$</annotation>\u0000 </semantics></math> of a big class <span></span><math>\u0000 <semantics>\u0000 <mi>α</mi>\u0000 <annotation>$alpha$</annotation>\u0000 </semantics></math> are zero.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 9","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70480","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148784969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The second moment of \u0000 \u0000 \u0000 \u0000 GL\u0000 4\u0000 \u0000 ×\u0000 \u0000 GL\u0000 2\u0000 \u0000 \u0000 $mathrm{GL}_4 times mathrm{GL}_2$\u0000 \u0000 \u0000 L\u0000 $L$\u0000 -functions at special points","authors":"Zhi Qi,&nbsp;Ruihua Qiao","doi":"10.1112/blms.70467","DOIUrl":"https://doi.org/10.1112/blms.70467","url":null,"abstract":"<p>In this paper, we provide an alternative proof of Chandee and Li's result on the second moment of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>GL</mi>\u0000 <mn>4</mn>\u0000 </msub>\u0000 <mo>×</mo>\u0000 <msub>\u0000 <mi>GL</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$ mathrm{GL}_4 times mathrm{GL}_2$</annotation>\u0000 </semantics></math> special <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math>-values. Our method is conceptually more direct as it neither detects the “Eisenstein–Kloosterman” cancelation nor uses the Poisson summation formula.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 9","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148784965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weighted geodesic restrictions of arithmetic eigenfunctions","authors":"Jiaqi Hou,&nbsp;Xiaoqi Huang","doi":"10.1112/blms.70469","DOIUrl":"https://doi.org/10.1112/blms.70469","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> be an arithmetic hyperbolic surface, <span></span><math>\u0000 <semantics>\u0000 <mi>ψ</mi>\u0000 <annotation>$psi$</annotation>\u0000 </semantics></math> a Hecke–Maass form, <span></span><math>\u0000 <semantics>\u0000 <mi>ℓ</mi>\u0000 <annotation>$ell$</annotation>\u0000 </semantics></math> a geodesic segment on <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math>, and <span></span><math>\u0000 <semantics>\u0000 <mi>μ</mi>\u0000 <annotation>$mu$</annotation>\u0000 </semantics></math> a Borel measure supported on <span></span><math>\u0000 <semantics>\u0000 <mi>ℓ</mi>\u0000 <annotation>$ell$</annotation>\u0000 </semantics></math> with dimension greater than 1/2. We obtain a power saving over the local bound of Eswarathasan and Pramanik for the <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$L^2$</annotation>\u0000 </semantics></math>-norm of <span></span><math>\u0000 <semantics>\u0000 <mi>ψ</mi>\u0000 <annotation>$psi$</annotation>\u0000 </semantics></math> with respect to <span></span><math>\u0000 <semantics>\u0000 <mi>μ</mi>\u0000 <annotation>$mu$</annotation>\u0000 </semantics></math>, which is a weighted generalization of Marshall's geodesic restriction bound and is proved by applying the method of arithmetic amplification. On a general two-dimensional Riemannian manifold, we also obtain a Kakeya–Nikodym bound for the <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$L^2$</annotation>\u0000 </semantics></math>-norm of any Laplace–Beltrami eigenfunction with respect to a Borel measure supported on a geodesic segment with dimension greater than 1/2.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 9","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148784968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Acylindrical visual splittings and the Tits alternative for Artin groups","authors":"William D. Cohen","doi":"10.1112/blms.70468","DOIUrl":"https://doi.org/10.1112/blms.70468","url":null,"abstract":"<p>We give a necessary and sufficient condition on a visual splitting of an Artin group satisfying the conclusions of two well-known conjectures to be acylindrical, and demonstrate how this can be used to provide a large class of novel examples of Artin groups that satisfy the Tits alternative.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 9","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70468","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148783914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"When weak convergence in von Neumann algebras implies almost uniform convergence?","authors":"Yerlan Nessipbayev,&nbsp;Fedor Sukochev,&nbsp;Dmitriy Zanin","doi":"10.1112/blms.70478","DOIUrl":"https://doi.org/10.1112/blms.70478","url":null,"abstract":"<p>We show that weak sequential convergence in a semifinite von Neumann algebra <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$mathcal {M}$</annotation>\u0000 </semantics></math> equipped with a faithful normal semifinite trace <span></span><math>\u0000 <semantics>\u0000 <mi>τ</mi>\u0000 <annotation>$tau$</annotation>\u0000 </semantics></math> implies almost uniform convergence if and only if <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$mathcal {M}$</annotation>\u0000 </semantics></math> is of type <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>I</mi>\u0000 <mi>fin</mi>\u0000 </msub>\u0000 <annotation>$mathrm{I}_{rm fin}$</annotation>\u0000 </semantics></math> with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>τ</mi>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 <mo>&lt;</mo>\u0000 <mi>∞</mi>\u0000 <mo>;</mo>\u0000 </mrow>\u0000 <annotation>$tau (mathbf {1})&lt;infty;$</annotation>\u0000 </semantics></math> and that weak sequential convergence in a finite von Neumann algebra <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$mathcal {M}$</annotation>\u0000 </semantics></math> with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>τ</mi>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 <mo>&lt;</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$tau (mathbf {1})&lt;infty$</annotation>\u0000 </semantics></math> implies (quasi-)norm convergence in noncommutative <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <annotation>$mathcal {L}_p$</annotation>\u0000 </semantics></math> spaces associated with <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$mathcal {M}$</annotation>\u0000 </semantics></math> for all <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 <mo>&lt;</mo>\u0000 <mi>p</mi>\u0000 <mo>&lt;</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$0&lt;p&lt;infty$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 9","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70478","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148784065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geometry of essential matrix ranges and the Smith–Ward problem for operator systems","authors":"Douglas Farenick,&nbsp;Chi-Kwong Li,&nbsp;Sushil Singla","doi":"10.1112/blms.70481","DOIUrl":"https://doi.org/10.1112/blms.70481","url":null,"abstract":"<p>A <span></span><math>\u0000 <semantics>\u0000 <mi>d</mi>\u0000 <annotation>$d$</annotation>\u0000 </semantics></math>-tuple of bounded linear selfadjoint operators acting on an infinite-dimensional separable Hilbert space is said to have the Smith–Ward property if the identity map of the image of the operator system in the Calkin algebra has a completely positive lift. In this paper, we focus on noncommutative geometric properties of a finite-dimensional operator system with the goal of understanding how geometric information encoded by the essential matrix range of a spanning set of a linear basis for the operator system implies the Smith–Ward property. Some geometric objects of special interest in this paper include one form of a noncommutative complex Euclidean ball and maximal noncommutative cubes and polydiscs, as well as some extremal compact matrix convex sets, <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>K</mi>\u0000 <mi>min</mi>\u0000 </msup>\u0000 <annotation>$K^{rm min}$</annotation>\u0000 </semantics></math> or <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>K</mi>\u0000 <mi>max</mi>\u0000 </msup>\u0000 <annotation>$K^{rm max}$</annotation>\u0000 </semantics></math>, determined by a given compact convex subset <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math> of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>d</mi>\u0000 </msup>\u0000 <annotation>$mathbb {R}^d$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 9","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70481","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148784216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity","authors":"Zhicheng Tong","doi":"10.1112/blms.70474","DOIUrl":"https://doi.org/10.1112/blms.70474","url":null,"abstract":"<p>Since Krengel's work [Monatsh. Math. <b>86</b> (1978/79), 3–6] in 1978, it has been widely known that no effective rate of convergence exists in the ergodic theorem. For toral translations, however, by choosing appropriate weights one can accelerate the convergence of ergodic averages to an exponential rate, but this intuitively requires both highly nonresonant frequencies and very regular observables. In this paper, we uncover a new phenomenon: Even for any given nonresonant frequency, there exists a nontrivial family of weights and observables of low regularity such that the weighted Birkhoff averages along quasi-periodic orbits converge at a quantitative, uniform, and exponential rate. This not only yields a finer understanding of the deep interaction between nonresonance and regularity in ergodic theory, but also stands as a weighted counterpart to a Yoccoz-type result [C. R. Acad. Sci. Paris Sér. A-B <b>291</b> (1980), A655–A658; Astérisque (1995), 89–242].</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 9","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148784215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A short proof of a central limit theorem for the order of the giant component and \u0000 \u0000 k\u0000 $k$\u0000 -core","authors":"Michael Anastos,&nbsp;Joshua Erde,&nbsp;Mihyun Kang,&nbsp;Vincent Pfenninger","doi":"10.1112/blms.70464","DOIUrl":"https://doi.org/10.1112/blms.70464","url":null,"abstract":"<p>In this note we outline a new and simple approach to proving central limit theorems for various ‘global’ graph parameters that have robust ‘local’ approximations, using the Efron–Stein inequality, which relies on a combinatorial analysis of the stability of these approximations under resampling an edge. As an application, we give short proofs of a central limit theorem for the order of the giant component and of the <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math>-core for sparse random graphs.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 8","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70464","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Kazdan–Warner obstructions for a fourth-order boundary problem","authors":"Sergio Cruz-Blázquez,&nbsp;Azahara DelaTorre","doi":"10.1112/blms.70461","DOIUrl":"https://doi.org/10.1112/blms.70461","url":null,"abstract":"<p>We derive Kazdan–Warner type identities for the boundary problem of prescribing nonconstant interior <span></span><math>\u0000 <semantics>\u0000 <mi>Q</mi>\u0000 <annotation>$Q$</annotation>\u0000 </semantics></math> curvature and boundary <span></span><math>\u0000 <semantics>\u0000 <mi>T</mi>\u0000 <annotation>$T$</annotation>\u0000 </semantics></math> curvature on the upper hemisphere <span></span><math>\u0000 <semantics>\u0000 <msubsup>\u0000 <mi>S</mi>\u0000 <mo>+</mo>\u0000 <mn>4</mn>\u0000 </msubsup>\u0000 <annotation>${mathbb {S}}^{4}_{+}$</annotation>\u0000 </semantics></math> by a conformal change of the standard metric. Using the natural variational formulation and conformal variations generated by boundary-preserving conformal vector fields, we obtain nontrivial integral obstructions to solvability.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 8","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70461","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148752451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}