Some characterizations of trivolutive Banach algebras

In this paper, we present a characterization of the closed ideal of a trivolutive Banach algebra (A; ).The main results are : a) the closed ideal I = Ker of a unital Banach algebra A is principle. b) For a commutative trivolutive algebra A, there is an idempotent u 2 A such that Ker = Iu in which Iu = fa 2 A; au = 0g. After that we investigate trivolutions on the Fourier-Stieltjes algebra B(G): Moreover, we study trivolutions on the algebra A B with -Lau product in relation to the corresponding one of A and B:

Keywords:

Trivolution , conditional expectation , group algebra.