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International Journal of Mathematics and Mathematical Sciences
Volume 16, Issue 4, Pages 819-822
http://dx.doi.org/10.1155/S0161171293001036

Comparisons between different spectra of an element in a Banach algebra

Dipartimento di Matematica dell'Università di Genova, Via L.B. Alberti 4, Genova 16132, Italy

Received 26 June 1990

Copyright © 1993 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

In this paper we study the relationships among the spectra of the cosets of an element of a Banach algebra in some quotient algebras. We also characterize the spectrum of any aM (where M is an ideal of a Banach algebra with identity and moreover has an identity) in the whole algebra in terms of the spectrum of a in M.