Polynomially Riesz elements

Abstract

A Banach algebra element ɑ ∈ A is said to be "polynomially Riesz", relative to the homomorphism T : A → B, if there exists a nonzero complex polynomial p(z) such that the image Tp(ɑ) ∈ B is quasinilpotent.

Keywords: Homomorphism of Banach algebras, polynomially Riesz element, Fredholm spectrum, Browder element, Browder spectrum.