Large C-polyhedrons in C-algebras

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-09-22 DOI:10.1016/j.topol.2025.109598

Clayton Suguio Hida

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引用次数: 0

Abstract

A classical polyhedron in a Banach space is a collection of points with a distinctive geometric separation property: each point in the set can be separated from the others by a closed convex set. This concept reflects the interplay between convexity and the geometry of Banach spaces. In this article, we introduce and study a noncommutative analogue of this notion, based on the concept of

C^{⁎}

-convexity, a generalization of classical convexity within the setting of

C^{⁎}

-algebras. We define the notion of a

C^{⁎}

-polyhedron as a family of elements in a

C^{⁎}

-algebra that satisfies a similar separation property with respect to closed

C^{⁎}

-convex sets. Our main goal is to investigate the maximal possible cardinality of

C^{⁎}

-polyhedrons in various

C^{⁎}

-algebras, with particular attention to classical examples from the theory of operator algebras, such as the algebras of compact and bounded operators on a Hilbert space.

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C*代数中的大C*多面体

Banach空间中的经典多面体是具有独特几何分离性质的点的集合：集合中的每个点都可以通过封闭凸集与其他点分离。这个概念反映了巴拿赫空间的凸性和几何之间的相互作用。在这篇文章中，我们引入并研究了这个概念的一个非交换的类比，基于C -凸性的概念，在C -代数的集合中经典凸性的推广。我们将C -多面体的概念定义为C -代数中满足关于闭C -凸集的类似分离性质的元素族。我们的主要目标是研究各种C -代数中C -多面体的最大可能基数，特别注意算子代数理论中的经典例子，例如Hilbert空间上的紧算子和有界算子代数。

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

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.