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Questions concerning matrix algebras and invariance of spectrum

Bruce A. Barnes
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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.

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Bruce A. Barnes. 2003-12-05. Questions concerning matrix algebras and invariance of spectrum. https://arxiv.org/abs/math/0312121

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