C*-convexity and C*-Polyhedron

Clayton Suguio Hida

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arXiv · 2306.03967

C-convexity and C-Polyhedron

Clayton Suguio Hida

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Abstract

A polyhedron in a Banach space is a family of points $\mathcal{X}$ such that for every $x\in \mathcal{X}$, there is a closed convex set $C$ such that $a\notin C$ and $\mathcal{X}\setminus\{x\}\subset C$. In this article, we consider the notion of C*-convexity and introduce the notion of a C*-polyhedron, which is a noncommutative version of the notion of polyhedrons. We investigate the largest size of a C*-polyhedron in some classical C*-algebras.

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Clayton Suguio Hida. 2023-06-06. C*-convexity and C*-Polyhedron. https://arxiv.org/abs/2306.03967

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