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Spectral properties of elements in different Banach algebras

Published online by Cambridge University Press:  18 May 2009

J. J. Grobler  and
H. Raubenheimer
J. J. Grobler
Affiliation:
Department of Mathematics and Applied Mathematics, Potchefstroom University for Christian Higher Education, Potchefstroom 2520, South Africa
H. Raubenheimer
Affiliation:
Department of Mathematics, University of the Orange Free State, Bloemfontein 9300, South Africa
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Let A be a Banach algebra with unit 1 and let B be a Banach algebra which is a subalgebra of A and which contains 1. In [5]Barnes gave sufficient conditions for B to be inverse closed in A. In this paper we consider single elements and study the question of how the spectrum relative to B of an element in B relates to the spectrum of the element relative to A.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 1 , January 1991 , pp. 11 - 20
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

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