Polynomially compact bilinear endorphisms of finite type of Banach algebras

Abstract

Kamowitz’s classical result on a compact endomorphism T of a commutative Ba- nach algebra A asserts that ∩T ∗n(Xr ) is finite where T ∗ is the adjoint of T and Xr),is the set of multiplicative linear functionals on A. This paper extends the underlying Kamowitz’s result to absolutely r-summing operators for 1 ™ r < ∞ or more generally polynomially compact endomorphisms as well as bilinear operators of finite type generated by Polynomially compact operators of a commutative Banach algebra. Keywords: Polynomial compactness; Endomorphism; Algebra; absolute summability; bilinear operators.