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Weakly Approximate Diagonalization of Homomorphisms into Finite von Neumann Algebras 进入有限冯-诺依曼代数的同态弱近似对角化
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-06-15 DOI: 10.1007/s10114-024-3260-5
Wen Hua Qian, Jun Hao Shen, Wen Ming Wu
{"title":"Weakly Approximate Diagonalization of Homomorphisms into Finite von Neumann Algebras","authors":"Wen Hua Qian,&nbsp;Jun Hao Shen,&nbsp;Wen Ming Wu","doi":"10.1007/s10114-024-3260-5","DOIUrl":"10.1007/s10114-024-3260-5","url":null,"abstract":"<div><p>Let <span>(cal{A})</span> be a unital C*-algebra and <span>(cal{B})</span> a unital C*-algebra with a faithful trace <i>τ</i>. Let <i>n</i> be a positive integer. We give the definition of weakly approximate diagonalization (with respect to <i>τ</i>) of a unital homomorphism <span>(phi:cal{A}rightarrow M_{n}(cal{B}))</span>. We give an equivalent characterization of McDuff II<sub>1</sub> factors. We show that, if <span>(cal{A})</span> is a unital nuclear C*-algebra and <span>(cal{B})</span> is a type II<sub>1</sub> factor with faithful trace <i>τ</i>, then every unital *-homomorphism <span>(phi:cal{A}rightarrow M_{n}(cal{B}))</span> is weakly approximately diagonalizable. If <span>(cal{B})</span> is a unital simple infinite dimensional separable nuclear C*-algebra, then any finitely many elements in <span>(M_{n}(cal{B}))</span> can be simultaneously weakly approximately diagonalized while the elements in the diagonals can be required to be the same.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411954","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}
引用次数: 0
Biderivations of Hom-Lie Algebras and Superalgebras 同列代数和超代数的双衍生
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-31 DOI: 10.1007/s10114-024-2121-6
La Mei Yuan, Jia Xin Li
{"title":"Biderivations of Hom-Lie Algebras and Superalgebras","authors":"La Mei Yuan, Jia Xin Li","doi":"10.1007/s10114-024-2121-6","DOIUrl":"https://doi.org/10.1007/s10114-024-2121-6","url":null,"abstract":"<p>On Hom-Lie algebras and superalgebras, we introduce the notions of biderivations and linear commuting maps, and compute them for some typical Hom-Lie algebras and superalgebras, including the <i>q</i>-deformed <i>W</i>(2,2) algebra, the <i>q</i>-deformed Witt algebra and superalgebra.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141194462","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}
引用次数: 0
The Faber Operator Acting on BMOA, BMO-Teichmüller Space and Chord-arc Curves 作用于 BMOA、BMO-Teichmüller 空间和弦弧曲线的法布尔算子
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-31 DOI: 10.1007/s10114-024-2184-4
Tai Liang Liu, Yu Liang Shen
{"title":"The Faber Operator Acting on BMOA, BMO-Teichmüller Space and Chord-arc Curves","authors":"Tai Liang Liu, Yu Liang Shen","doi":"10.1007/s10114-024-2184-4","DOIUrl":"https://doi.org/10.1007/s10114-024-2184-4","url":null,"abstract":"<p>After reviewing Grunsky operator and Faber operator acting on Dirichlet space, we discuss the boundedness of Faber operator on BMOA, a new subject which turns out to be closely related to the BMO theory of the universal Teichmüller space. In particular, we show that the Faber operator acts as a bounded operator on BMOA if the symbol conformal map stays nearly to the base point in the BMO-Teichmüller space. Meanwhile, we obtain several results on quasiconformal mappings, BMO-Teichmüller space and chord-arc curves as well. As by-products, this provides a complex analysis approach to the boundedness of the Cauchy integral acting on BMO functions on a chord-arc curve near to the unit circle in the BMO-Teichmüller space.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141194380","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}
引用次数: 0
Eigenvalues for the Clamped Plate Problem of (mathfrak{L}_{nu}^{2}) Operator on Complete Riemannian Manifolds 完全黎曼曼体上 $$mathfrak{L}_{nu}^{2}$ 算子的夹板问题特征值
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-31 DOI: 10.1007/s10114-024-1697-1
Ling Zhong Zeng
{"title":"Eigenvalues for the Clamped Plate Problem of (mathfrak{L}_{nu}^{2}) Operator on Complete Riemannian Manifolds","authors":"Ling Zhong Zeng","doi":"10.1007/s10114-024-1697-1","DOIUrl":"10.1007/s10114-024-1697-1","url":null,"abstract":"<div><p><span>(mathfrak{L}_{nu})</span> operator is an important extrinsic differential operator of divergence type and has profound geometric settings. In this paper, we consider the clamped plate problem of <span>(mathfrak{L}_{nu}^{2})</span> operator on a bounded domain of the complete Riemannian manifolds. A general formula of eigenvalues of <span>(mathfrak{L}_{nu}^{2})</span> operator is established. Applying this general formula, we obtain some estimates for the eigenvalues with higher order on the complete Riemannian manifolds. As several fascinating applications, we discuss this eigenvalue problem on the complete translating solitons, minimal submanifolds on the Euclidean space, submanifolds on the unit sphere and projective spaces. In particular, we get a universal inequality with respect to the <span>(mathcal{L}_{II})</span> operator on the translating solitons. Usually, it is very difficult to get universal inequalities for weighted Laplacian and even Laplacian on the complete Riemannian manifolds. Therefore, this work can be viewed as a new contribution to universal estimate.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141194509","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}
引用次数: 0
Noise Effect on the 2D Stochastic Burgers Equation 噪声对二维随机布尔格斯方程的影响
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-31 DOI: 10.1007/s10114-024-3079-0
Zhao Dong, Jiang Lun Wu, Guo Li Zhou
{"title":"Noise Effect on the 2D Stochastic Burgers Equation","authors":"Zhao Dong,&nbsp;Jiang Lun Wu,&nbsp;Guo Li Zhou","doi":"10.1007/s10114-024-3079-0","DOIUrl":"10.1007/s10114-024-3079-0","url":null,"abstract":"<div><p>By comprehensive utilizing of the geometry structure of 2D Burgers equation and the stochastic noise, we find the decay properties of the solution to the stochastic 2D Burgers equation with Dirichlet boundary conditions. Consequently, the expected ergodicity for this turbulence model is established.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141194278","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}
引用次数: 0
Deformation of Rigid Conjugate Self-dual Galois Representations 刚性共轭自偶伽罗瓦表示的变形
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-31 DOI: 10.1007/s10114-024-1409-x
Yi Feng Liu, Yi Chao Tian, Liang Xiao, Wei Zhang, Xin Wen Zhu
{"title":"Deformation of Rigid Conjugate Self-dual Galois Representations","authors":"Yi Feng Liu,&nbsp;Yi Chao Tian,&nbsp;Liang Xiao,&nbsp;Wei Zhang,&nbsp;Xin Wen Zhu","doi":"10.1007/s10114-024-1409-x","DOIUrl":"10.1007/s10114-024-1409-x","url":null,"abstract":"<div><p>In this article, we study deformations of conjugate self-dual Galois representations. The study is twofold. First, we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite field, satisfying a certain property called rigid. Second, we study the rigidity property for the family of residue Galois representations attached to a symmetric power of an elliptic curve, as well as to a regular algebraic conjugate self-dual cuspidal representation.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141194345","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}
引用次数: 0
The Essential 2-rank for Classical Groups 经典群的基本 2 级
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-31 DOI: 10.1007/s10114-024-1494-x
Jian Bei An, Yong Xu
{"title":"The Essential 2-rank for Classical Groups","authors":"Jian Bei An,&nbsp;Yong Xu","doi":"10.1007/s10114-024-1494-x","DOIUrl":"10.1007/s10114-024-1494-x","url":null,"abstract":"<div><p>Let <i>G</i> be a symplectic or orthogonal group defined over a finite field with odd characteristic and let <i>D</i> ≤ <i>G</i> be a Sylow 2-subgroup. In this paper, we classify the essential 2-subgroups and determine the essential 2-rank of the Frobenius category <i>ℱ</i><sub><i>D</i></sub>(<i>G</i>). Together with the results of An-Dietrich and Cao–An–Zeng, this completes the work of essential subgroups and essential ranks of classical groups.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141194367","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}
引用次数: 0
A Weighted Flow related to a Trudinger-Moser Functional on Closed Riemann Surface 封闭黎曼面上与特鲁丁格-莫泽函数相关的加权流
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-20 DOI: 10.1007/s10114-024-2447-0
Peng Xiu Yu
{"title":"A Weighted Flow related to a Trudinger-Moser Functional on Closed Riemann Surface","authors":"Peng Xiu Yu","doi":"10.1007/s10114-024-2447-0","DOIUrl":"10.1007/s10114-024-2447-0","url":null,"abstract":"<div><p>In this paper, with (Σ, <i>g</i>) being a closed Riemann surface, we analyze the possible concentration behavior of a heat flow related to the Trudinger-Moser energy. We obtain a long time existence for the flow. And along some sequence of times <i>t</i><sub><i>k</i></sub> → + ∞, we can deduce the convergence of the flow in <i>H</i><sup>2</sup>(Σ). Furthermore, the limit function is a critical point of the Trudinger-Moser functional under certain constraint.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141122001","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}
引用次数: 0
On the Monge-Kantorovich Mass Transfer Problem in Higher Dimensions 论更高维度的蒙日-康托洛维奇传质问题
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-20 DOI: 10.1007/s10114-024-2628-x
Xiao Jun Lu
{"title":"On the Monge-Kantorovich Mass Transfer Problem in Higher Dimensions","authors":"Xiao Jun Lu","doi":"10.1007/s10114-024-2628-x","DOIUrl":"10.1007/s10114-024-2628-x","url":null,"abstract":"<div><p>This paper mainly investigates the approximation of a global maximizer of the Monge-Kantorovich mass transfer problem in higher dimensions through the approach of nonlinear partial differential equations with Dirichlet boundary. Using an approximation mechanism, the primal maximization problem can be transformed into a sequence of minimization problems. By applying the systematic canonical duality theory, one is able to derive a sequence of analytic solutions for the minimization problems. In the final analysis, the convergence of the sequence to an analytical global maximizer of the primal Monge-Kantorovich problem will be demonstrated.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141123395","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}
引用次数: 0
The Orthogonal Bases of Exponential Functions Based on Moran-Sierpinski Measures 基于 Moran-Sierpinski 测量的指数函数正交基
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-20 DOI: 10.1007/s10114-024-2604-5
Qi Rong Deng, Xing Gang He, Ming Tian Li, Yuan Ling Ye
{"title":"The Orthogonal Bases of Exponential Functions Based on Moran-Sierpinski Measures","authors":"Qi Rong Deng,&nbsp;Xing Gang He,&nbsp;Ming Tian Li,&nbsp;Yuan Ling Ye","doi":"10.1007/s10114-024-2604-5","DOIUrl":"10.1007/s10114-024-2604-5","url":null,"abstract":"<div><p>Let <i>A</i><sub><i>n</i></sub> ∈ <i>M</i><sub>2</sub> (ℤ) be integral matrices such that the infinite convolution of Dirac measures with equal weights</p><div><div><span>$$mu_{{A_{n},ngeq1}}:=delta_{A_{1}^{-1}cal{D}}astdelta_{A_{1}^{-1}A_{2}^{-2}cal{D}}astcdots$$</span></div></div><p> is a probability measure with compact support, where <span>(cal{D}={(0,0)^{t},(1,0)^{t},(0,1)^{t}})</span> is the Sierpinski digit. We prove that there exists a set Λ ⊂ ℝ<sup>2</sup> such that the family {e<sup>2<i>π</i>i〈λ,<i>x</i>〉</sup>: λ ∈ Λ} is an orthonormal basis of <span>(L^{2}(mu_{{A_{n},ngeq1}}))</span> if and only if <span>({1over{3}}(1,-1)A_{n}inmathbb{Z}^{2})</span> for <i>n</i> ≥ 2 under some metric conditions on <i>A</i><sub><i>n</i></sub>.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141119794","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}
引用次数: 0
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