Decomposition of H*-Algebra Valued Negative Definite Functions on Topological *-Semigroups

In the present paper, among other results, a decomposition formula is given for the w-bounded continuous negative definite functions of a topological *-semigroup S with a weight function w into a proper H*-algebra A in terms of w-bounded continuous positive definite A-valued functions on S. A generalization of a well-known result of K. Harzallah is obtained. An earlier conjecture of the author is also established.

In the present paper, among other results, a decomposition formula is given for the w-bounded continuous negative definite functions of a topological * semigroup S with a weight function w into a proper H*-algebra A in terms of w bounded continuous positive definite A-valued functions on S. A generalization of a well-known result of K. Harzallah is obtained. An earlier conjecture of the author is also established.