Questions concerning matrix algebras and invariance of spectrum

Bruce A. Barnes

paper

Questions concerning matrix algebras and invariance of spectrum

arXiv:math/0312121

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.

6 pages, no figures, no tables