The multiplier algebra and BSE property of the direct sum of Banach algebras (Q2865128)

The paper deals with the properties of BSE algebras, named after Bochner, Schoenberg and Eberlein. The authors prove that the direct sum of two commutative semisimple Banach algebras \(A\) and \(B\) is a BSE algebra if and only if both \(A\) and \(B\) are BSE algebras. They also prove that, if the \(\theta\)-Lau product of a commutative Banach algebra \(A\) and a unital commutative Banach algebra \(B\) is a BSE algebra, then \(B\) is a BSE algebra as well. They also provide examples which show that one cannot conclude that \(A\) must be a BSE algebra if \(A\) is not a unital algebra.