Banach–Mazur stability of von Neumann algebras

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Topology and Analysis Pub Date : 2020-12-11 DOI:10.1142/s1793525321500151

J. Roydor

引用次数: 0

Abstract

We initiate the study of perturbation of von Neumann algebras relatively to the Banach–Mazur distance. We first prove that the type decomposition is continuous, i.e. if two von Neumann algebras are close, then their respective summands of each type are close. We then prove that, under some vanishing conditions on its Hochschild cohomology groups, a von Neumann algebra is Banach–Mazur stable, i.e. any von Neumann algebra which is close enough is actually Jordan ∗-isomorphic. These vanishing conditions are possibly empty.

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von Neumann代数的Banach-Mazur稳定性

我们开始研究相对于Banach-Mazur距离的von Neumann代数的摄动。我们首先证明了类型分解是连续的，即如果两个von Neumann代数是接近的，则它们各自的和是接近的。然后证明了在其Hochschild上同调群上的某些消失条件下，von Neumann代数是Banach-Mazur稳定的，即任何足够接近的von Neumann代数实际上是Jordan * -同构的。这些消失的条件可能是空的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Topology and Analysis MATHEMATICS-

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is devoted to topology and analysis, broadly defined to include, for instance, differential geometry, geometric topology, geometric analysis, geometric group theory, index theory, noncommutative geometry, and aspects of probability on discrete structures, and geometry of Banach spaces. We welcome all excellent papers that have a geometric and/or analytic flavor that fosters the interactions between these fields. Papers published in this journal should break new ground or represent definitive progress on problems of current interest. On rare occasion, we will also accept survey papers.