基于框架理论的\(C^*\) -代数中的厚元与厚态

IF 1.7 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2023-06-18 DOI:10.1134/S106192082302005X

D. V. Fufaev

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引用次数: 0

摘要

研究了若干类非交换\(C^*\) -代数，并在拓扑学上推广了原来关于交换代数的一些结果。特别地，我们对具有接近可分性和\( \sigma \) -紧性的拓扑空间的结果感兴趣。为了得到相应性质的代数非交换版本，我们定义并使用了厚元素和状态的概念。特别地，如果一个元素与它正交的唯一元素为零，它就是厚元素。

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Thick Elements and States in \(C^*\)-Algebras in View of Frame Theory

We study some classes of noncommutative \(C^*\)-algebras and generalize some results which were originally obtained for commutative algebras in topological terms. In particular, we are interested in results obtained for topological spaces with properties close to separability and \( \sigma \)-compactness. To obtain the algebraic, noncommutative versions of corresponding properties, we define and use the notions of thick elements and states. In particular, an element is thick if the only element orthogonal to it is zero.

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.