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)g = sup{|λ| : ∈ 2 σ S(a)}

for all a ∈ A.

Mathematics Subject Classification (2010): 46H05, 47A10, 47A53

Keywords: Regularities, semiregularities, Weyl spectrum, Browder spectrum