Completely positive invariant conjugate-bilinear maps in partial *-algebras

TL;DR

This paper introduces a new class of maps in partial *-algebras, proves a generalized Stinespring theorem for them, and explores their applications in extending *-representations in certain algebraic structures.

Contribution

It defines completely positive invariant conjugate-bilinear maps in partial *-algebras and establishes a generalized Stinespring theorem, advancing the theory of *-algebra representations.

Findings

Established a generalized Stinespring theorem for these maps

Proved the existence of integrable extensions of *-representations

Extended the framework for partial *-algebras and their representations

Abstract

The notion of completely positive invariant conjugate-bilinear map in a partial *-algebra is introduced and a generalized Stinespring theorem is proven. Applications to the existence of integrable extensions of *-representations of commutative, locally convex quasi*-algebras are also discussed.