Radius preserving (semi)regularities in Banach algebras

Abstract

In this note we investigate regularities (semiregularities) R and S in a Banach algebra A satisfying S ? R and the corresponding spectra σ_S and σ_R Satisfying

sup {|λ| : λ ∈ σ_R(a)} = sup{|λ| : λ ∈ σ_S (a)}