Questions concerning matrix algebras and invariance of spectrum

Bruce A. Barnes

Questions concerning matrix algebras and invariance of spectrum

Functional Analysis 2007-05-23 v1

Authors: Bruce A. Barnes

Abstract

Let $A$ and $B$ be unital Banach algebras with $A$ a subalgebra of $B$ . Denote the algebra of all $n\times n$ matrices with entries from $A$ by $M_{n}(A)$ . In this paper we prove some results concerning the open question: If $A$ is inverse closed in $B$ , then is $M_{n}(A)$ inverse closed in $M_{n}(B)$ ? We also study related questions in the setting where $A$ is a symmetric Banach *-algebra.

Keywords

matrix algebras banach algebras inverse closed spectrum invariance symmetric banach *-algebra

Cite

@article{arxiv.math/0312121,
  title  = {Questions concerning matrix algebras and invariance of spectrum},
  author = {Bruce A. Barnes},
  journal= {arXiv preprint arXiv:math/0312121},
  year   = {2007}
}

Comments

6 pages, no figures, no tables

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