International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 4, Pages 819-822
doi:10.1155/S0161171293001036

Comparisons between different spectra of an element in a Banach algebra

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 a∈M (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.