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Questions concerning matrix algebras and invariance of spectrum

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Abstract

LetA andB be unital Banach algebras withA a subalgebra ofB. Denote the algebra of alln xn matrices with entries fromA byM n (A). In this paper we prove some results concerning the open question: IfA is inverse closed inB, then isM n (A) inverse closed inM n (B)? We also study related questions in the setting where A is a symmetric Banach *-algebra.

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Authors and Affiliations

  1. Department of Mathematics, University of Oregon, 97403, Eugene, Oregon, USA

    Bruce A. Barnes

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  1. Bruce A. Barnes
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Correspondence to Bruce A. Barnes.

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Dedicated to Professor Ashoke K. Roy on his retirement.

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Barnes, B.A. Questions concerning matrix algebras and invariance of spectrum. Proc. Indian Acad. Sci. (Math. Sci.) 113, 71–76 (2003). https://doi.org/10.1007/BF02829680

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  • DOI: https://doi.org/10.1007/BF02829680

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