SOME ASPECTS ON REPRESENTATION THEORY OF INVOLUTIVE GROUP ALGEBRAS

Abstract

Let A be a separable C*-algebra and G1 and G2 be two locally compact groups. We consider two C*-dynamical
systems (A, G1, ) and (A, G2, ) with two states f and g which are stationary for the group morphisms  and 
respectively. Let Hf and Hg be the associated Hilbert spaces and L1(G1, A; ) and L1(G2, A; ) be the involutive
group algebras. For every element u in H f  H g, we obtain a positive form  on the projective tensor product
of L1(G1, A; ) and L1(G2, A; ). Again, for two specific left ideals N1j and N2 j of L1(G1, A; ) and L1(G2, A; )
respectively, we show that (N1j  N2j)+(N1j* N2j*) is contained in ker .