BSE Banach modules and multipliers (Q1340822)

The author introduces a class of Banach modules which are a module version of the BSE commutative Banach algebras considered by the author and Hatori. A Banach module which belongs to this class is called a BSE. Every multiplier of a BSE Banach \(A\)-module can be characterized as a continuous vector field on the carrier space of \(A\) which satisfies a Bochner-Schoenberg-Eberlein-type inequality. The author gives typical BSE Banach modules with respect to \(C^*\)-algebras and convolution algebras. He also shows that any Banach \(A\)-module is BSE whenever \(A\) is a commutative \(C^*\)-algebra with discrete carrier space.