Comparisons between different spectra of an element in a Banach algebra (Q689044)

Summary: 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 \({\mathbf a}\in M\) (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 \({\mathbf a}\) in \(M\).