The Bochner–Schoenberg–Eberlein Property and Spectral Synthesis for Certain Banach Algebra Products

Abstract

AbstractAssociated with two commutative Banach algebras A and B and a character θ of B is a certain Banach algebra product A ×θB, which is a splitting extension of B by A. We investigate two topics for the algebra A ×θB in relation to the corresponding ones of A and B. The first one is the Bochner–Schoenberg–Eberlein property and the algebra of Bochner–Schoenberg–Eberlein functions on the spectrum, whereas the second one concerns the wide range of spectral synthesis problems for A ×θB.