On Group Von Neumann Algebras with Vector-Valued Functions

Abstract

Let be a locally compact group equipped with a normalized Haar measure , ( ) the Fourier algebra of and ( ) the von Neumann algebra generated by the left regular representation of . In this paper, we introduce the space ( , ) associated with the Fourier algebra ( , ) for vector-valued functions on G, where is a * -algebra. Some basic properties are discussed in the category of Banach space, and also in the category of operator space.