Questions concerning matrix algebras and invariance of spectrum

Questions concerning matrix algebras and invariance of spectrum

LetA andB be unital Banach algebras withA a subalgebra ofB. Denote the algebra of alln xn matrices with entries fromA byMn (A). In this paper we prove some results concerning the open question: IfA is inverse closed inB, then isMn (A) inverse closed inMn (B)? We also study related questions in the s...

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Veröffentlicht in:Proceedings of the Indian Academy of Sciences. Mathematical sciences 2003-02, Vol.113 (1), p.71-76
1. Verfasser: Barnes, Bruce A.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
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Zusammenfassung:LetA andB be unital Banach algebras withA a subalgebra ofB. Denote the algebra of alln xn matrices with entries fromA byMn (A). In this paper we prove some results concerning the open question: IfA is inverse closed inB, then isMn (A) inverse closed inMn (B)? We also study related questions in the setting where A is a symmetric Banach *-algebra.
ISSN:0253-4142
0973-7685
DOI:10.1007/BF02829680