Journal of Functional Analysis最新文献

{"title":"Voiculescu's theorem in properly infinite factors","authors":"Donald Hadwin ,&nbsp;Minghui Ma ,&nbsp;Junhao Shen","doi":"10.1016/j.jfa.2025.111198","DOIUrl":"10.1016/j.jfa.2025.111198","url":null,"abstract":"<div><div>In this paper, we investigate Voiculescu's theorem on approximate unitary equivalence in separable properly infinite factors. As applications, we establish the norm-denseness of the set of all reducible operators, prove a generalized Voiculescu's bicommutant theorem and a version of asymptotic bicommutant theorem, and obtain an interesting cohomological result. Additionally, we extend these results to multiplier algebras within separable type III factors. At last, a concept of the nuclear length is introduced.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111198"},"PeriodicalIF":1.6,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145154381","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":"On the converse of Prékopa's theorem and Berndtsson's theorem","authors":"Wang Xu ,&nbsp;Hui Yang","doi":"10.1016/j.jfa.2025.111214","DOIUrl":"10.1016/j.jfa.2025.111214","url":null,"abstract":"<div><div>Extending the framework of the converse <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> theory, we establish converse results for Berndtsson's theorem on the plurisubharmonic variation of Bergman kernels, showing that both the plurisubharmonicity of functions and the pseudoconvexity of domains are necessary conditions in twisted senses. We also prove analogous results for Prékopa's theorem from convex analysis.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111214"},"PeriodicalIF":1.6,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155322","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":"A martingale approach to noncommutative stochastic calculus","authors":"David A. Jekel ,&nbsp;Todd A. Kemp ,&nbsp;Evangelos A. Nikitopoulos","doi":"10.1016/j.jfa.2025.111200","DOIUrl":"10.1016/j.jfa.2025.111200","url":null,"abstract":"<div><div>We present a new approach to noncommutative stochastic calculus that is, like the classical theory, based primarily on the martingale property. Using this approach, we introduce a general theory of stochastic integration and quadratic (co)variation for a certain class of noncommutative processes, analogous to semimartingales, that includes both the <em>q</em>-Brownian motions and classical matrix-valued Brownian motions. As applications, we obtain Burkholder–Davis–Gundy inequalities (with <span><math><mi>p</mi><mo>≥</mo><mn>2</mn></math></span>) for continuous-time noncommutative martingales and a noncommutative Itô's formula for “adapted <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> maps,” including trace ⁎-polynomial maps and operator functions associated to the noncommutative <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> scalar functions <span><math><mi>R</mi><mo>→</mo><mi>C</mi></math></span> introduced by Nikitopoulos, as well as the more general multivariate tracial noncommutative <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> functions introduced by Jekel, Li, and Shlyakhtenko.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 2","pages":"Article 111200"},"PeriodicalIF":1.6,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222822","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":"(INV) condition and regularity of the inverse","authors":"Anna Doležalová ,&nbsp;Stanislav Hencl ,&nbsp;Jani Onninen","doi":"10.1016/j.jfa.2025.111215","DOIUrl":"10.1016/j.jfa.2025.111215","url":null,"abstract":"<div><div>Let <span><math><mi>f</mi><mo>:</mo><mi>Ω</mi><mo>→</mo><msup><mrow><mi>Ω</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> be a Sobolev mapping of finite distortion between planar domains Ω and <span><math><msup><mrow><mi>Ω</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span>, satisfying the <span><math><mo>(</mo><mi>I</mi><mi>N</mi><mi>V</mi><mo>)</mo></math></span> condition and coinciding with a homeomorphism near ∂Ω. We show that <em>f</em> admits a generalized inverse mapping <span><math><mi>h</mi><mo>:</mo><msup><mrow><mi>Ω</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>→</mo><mi>Ω</mi></math></span>, which is also a Sobolev mapping of finite distortion and satisfies the <span><math><mo>(</mo><mi>I</mi><mi>N</mi><mi>V</mi><mo>)</mo></math></span> condition.</div><div>We also establish a higher-dimensional analogue of this result: if a mapping <span><math><mi>f</mi><mo>:</mo><mi>Ω</mi><mo>→</mo><msup><mrow><mi>Ω</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> of finite distortion is in the Sobolev class <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>p</mi></mrow></msup><mo>(</mo><mi>Ω</mi><mo>,</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> with <span><math><mi>p</mi><mo>&gt;</mo><mi>n</mi><mo>−</mo><mn>1</mn></math></span> and satisfies the <span><math><mo>(</mo><mi>I</mi><mi>N</mi><mi>V</mi><mo>)</mo></math></span> condition, then <em>f</em> has an inverse in <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup><mo>(</mo><msup><mrow><mi>Ω</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>,</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> that is also of finite distortion.</div><div>Furthermore, we characterize Sobolev mappings satisfying <span><math><mo>(</mo><mi>I</mi><mi>N</mi><mi>V</mi><mo>)</mo></math></span> whose generalized inverses have finite <em>n</em>-harmonic energy.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111215"},"PeriodicalIF":1.6,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155319","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":"On the emergence of almost-honeycomb structures in low-energy planar clusters","authors":"M. Caroccia ,&nbsp;K. DeMason ,&nbsp;F. Maggi","doi":"10.1016/j.jfa.2025.111205","DOIUrl":"10.1016/j.jfa.2025.111205","url":null,"abstract":"<div><div>Several commonly observed physical and biological systems are arranged in shapes that closely resemble an honeycomb cluster, that is, a tessellation of the plane by regular hexagons. Although these shapes are not always the direct product of energy minimization, they can still be understood, at least phenomenologically, as low-energy configurations. In this paper, explicit quantitative estimates on the geometry of such low-energy configurations are provided, showing in particular that the vast majority of the chambers must be generalized polygons with six edges, and be closely resembling regular hexagons. Part of our arguments is a detailed revision of the estimates behind the global isoperimetric principle for honeycomb clusters due to Hales <span><span>[6]</span></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 2","pages":"Article 111205"},"PeriodicalIF":1.6,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157140","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":"Nakano positivity of singular Hermitian metrics: Approximations and applications","authors":"Takahiro Inayama ,&nbsp;Shin-ichi Matsumura","doi":"10.1016/j.jfa.2025.111206","DOIUrl":"10.1016/j.jfa.2025.111206","url":null,"abstract":"<div><div>This paper studies the approximation of singular Hermitian metrics on vector bundles using smooth Hermitian metrics with Nakano semi-positive curvature on Zariski open sets. We show that singular Hermitian metrics capable of this approximation satisfy Nakano semi-positivity as defined through the <span><math><mover><mrow><mo>∂</mo></mrow><mo>‾</mo></mover></math></span>-equation with optimal <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-estimates. Furthermore, for a projective fibration <span><math><mi>f</mi><mo>:</mo><mi>X</mi><mo>→</mo><mi>Y</mi></math></span> with a line bundle <em>L</em> on <em>X</em>, we provide a specific condition under which the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-metric on the direct image sheaf <span><math><msub><mrow><mi>f</mi></mrow><mrow><mo>⁎</mo></mrow></msub><msub><mrow><mi>O</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>X</mi><mo>/</mo><mi>Y</mi></mrow></msub><mo>+</mo><mi>L</mi><mo>)</mo></math></span> admits this approximation. As an application, we establish several vanishing theorems.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111206"},"PeriodicalIF":1.6,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145118844","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":"Minimal Lagrangian surfaces with Legendrian capillary boundary in S2×S2","authors":"Mingyan Li","doi":"10.1016/j.jfa.2025.111207","DOIUrl":"10.1016/j.jfa.2025.111207","url":null,"abstract":"<div><div>In this paper we study minimal Lagrangian surfaces in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> with Legendrian capillary boundary on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>. We prove that such surfaces must be of annulus type and they are congruent to the totally geodesic Lagrangian torus.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 2","pages":"Article 111207"},"PeriodicalIF":1.6,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145134758","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":"Schoenberg correspondence for multifaced independence","authors":"Malte Gerhold","doi":"10.1016/j.jfa.2025.111212","DOIUrl":"10.1016/j.jfa.2025.111212","url":null,"abstract":"<div><div>We extend the Schoenberg correspondence for universal independences by Schürmann &amp; Voß to the multivariate setting of Manzel &amp; Schürmann, covering, e.g., Voiculescu's bifreeness as well as Bożejko &amp; Speicher's c-free independence. At the same time, we free the proof in the univariate situation from its dependence on Muraki's “5 Independences Theorem”.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111212"},"PeriodicalIF":1.6,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155732","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":"Solutions to SU(n + 1) Toda system generated by spherical metrics","authors":"Yiqian Shi ,&nbsp;Chunhui Wei ,&nbsp;Bin Xu","doi":"10.1016/j.jfa.2025.111197","DOIUrl":"10.1016/j.jfa.2025.111197","url":null,"abstract":"<div><div>Following A.B. Givental (1989) <span><span>[5]</span></span>, we refer to an <em>n</em>-tuple <span><math><mo>(</mo><msub><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>ω</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span> of Kähler forms on a Riemann surface <em>S</em> as a <em>solution to the</em> SU<span><math><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span> <em>Toda system</em> if and only if<span><span><span><math><mo>(</mo><mrow><mi>Ric</mi></mrow><mo>(</mo><msub><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo><mo>,</mo><mo>…</mo><mo>,</mo><mrow><mi>Ric</mi></mrow><mo>(</mo><msub><mrow><mi>ω</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo><mo>)</mo><mo>=</mo><mo>(</mo><mn>2</mn><msub><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><mn>2</mn><msub><mrow><mi>ω</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo></math></span></span></span> where <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> is the Cartan matrix of type <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. In particular, when <span><math><mi>n</mi><mo>=</mo><mn>1</mn></math></span>, this solution corresponds to a spherical metric. Using the correspondence between solutions and totally unramified unitary curves, we show that a spherical metric <em>ω</em> generates a family of solutions, including <span><math><msubsup><mrow><mo>(</mo><mi>i</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>−</mo><mi>i</mi><mo>)</mo><mi>ω</mi><mo>)</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup></math></span>. Moreover, we characterize this family in terms of the monodromy group of the spherical metric. As a consequence, we obtain a new solution class to the SU<span><math><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span> Toda system with cone singularities on compact Riemann surfaces, complementing the existence results of Lin et al. (2020) <span><span>[9]</span></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111197"},"PeriodicalIF":1.6,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155321","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":"Curvature pinching estimate under the Laplacian G2 flow","authors":"Chuanhuan Li ,&nbsp;Yi Li","doi":"10.1016/j.jfa.2025.111199","DOIUrl":"10.1016/j.jfa.2025.111199","url":null,"abstract":"<div><div>In this paper, we derive a pinching estimate for the traceless Ricci curvature in terms of scalar curvature and the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norm of the Weyl tensor under the Laplacian <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> flow for closed <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> structures. Then we apply this estimate to study the long time existence of the Laplacian <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> flow and prove that the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norm of the Weyl tensor has to blow up at least at a certain rate under bounded scalar curvature.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111199"},"PeriodicalIF":1.6,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155318","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}