On Group Von Neumann Algebras with Vector-Valued Functions

Abstract

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