Fourier-Stieltjes Algebra And Its Properties

LetG be a locally compact group,and B (G )be the Fourier-Stieltjes algebra of G .This article mainly summary the basic knowledge of B (G ).Firstly, we prove that B (G )is a communicative Banach algebra. Secondly, let H be a closed normal subgroup ofG ,we discuss the relationship between B ( H ), B ( G / H )and B ( G ),but we can't obtain the result that B (G / H ) ??j→B (G ) ?h?→B ( H)is also a short exact sequence.At last,we discuss the relationship between B (G )and A( G ).