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International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 4, Pages 823-824
http://dx.doi.org/10.1155/S016117128900102X

Supersets for the spectrum of elements in extended Banach algebras

Division of Natural Sciences, Lewis Clark College, Lewiston 83501, ID, USA

Received 1 June 1987; Revised 21 October 1987

Copyright © 1989 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

If A is a Banach Algebra with or without an identity, A can be always extended to a Banach algebra A¯ with identity, where A¯ is simply the direct sum of A and C, the algebra of complex numbers. In this note we find supersets for the spectrum of elements of A¯.