Topological radicals, V. From algebra to spectral theory

2012/08/22 by Victor S. Shulman, Shulman, Victor S., Yuri V. Turovskii +1 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1208.4609

openalex publication_date 2012/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce and study procedures and constructions in the theory of the joint spectral radius that are related to the spectral theory. In particular we devlop the theory of the scattered radical. Among applications we find some sufficient conditions of continuity of the spectrum and spectral radii of various types, and prove that in GCR C*-algebras the joint spectral radius is continuous on precompact subsets and coincides with the Berger-Wang radius.

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