No abstract

This work addresses an extension of Fourier-Stieltjes transform of a vector measure defined on compact groups to locally compact groups, by using a group representation induced by a representation of one of its compact subgroups.

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.