Questions concerning matrix algebras and invariance of spectrum

Details Questions concerning matrix algebras and invariance of spectrum Questions concerning matrix algebras and invariance of spectrum

2003-12-05

arxiv.org/abs/math/0312121v1

Proc. Indian Acad. Sci. (Math. Sci.), Vol. 113, No. 1, February 2003, pp. 71-76

Mathematics

Functional Analysis

6 pages, no figures, no tables

Scientific paper

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.

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