Representations of ∗-Semigroups Associated to Invariant Kernels and Seminormed ∗-Subalgebras with Symmetric Generators of C^*-Algebras

Abstract

We show the inverse limits, the positive definite kernels, the dual spaces and the topological representation of C^*-algebras with maps between locally C^*-algebras and seminormed ∗-subalgebras of l^∞. The representations of Hermitian kernels by means of Krein spaces and of ∗-semigroups associated to invariant kernels with values adjointable and application of Jacobi representation convex topological R-algebras and the dilations of some VH-spaces operator valued kernels are considered. We give some new classes, a canonical decomposition, an approximation of unitary equivalence and a C^*-algebra approach to complex and skew symmetric operators. We determine and characterize the C^*-algebras with Hausdorff spectrum and complex symmetric generators of C^* -algebras.