Multiplier algebras, Banach bundles, and one-parameter semigroups

Abstract

Several results are proved concerning representations of multiplier algebras that arise as extensions of representations of underlying Banach algebras. These results are then used to rederive Kisynski's generalisation of the Hille-Yosida theorem and to establish two generalisations of the Trotter-Kato theorem, one of which, involving Banach bundles, is abstract and the other is classical in character.