Quasi-representations of Finsler modules over C*-algebras

TL;DR

This paper demonstrates that Finsler modules over C*-algebras can be quasi-represented in operator spaces, introduces a notion of completely positive morphisms, and establishes a Stinespring type theorem for these modules.

Contribution

It introduces the concept of quasi-representations for Finsler modules over C*-algebras and proves a Stinespring type theorem in this context.

Findings

Every Finsler module admits a quasi-representation into bounded operators.

Defined completely positive φ-morphisms and proved a Stinespring type theorem.

Analyzed nondegeneracy and irreducibility of quasi-representations.

Abstract

We show that every Finsler module over a $C^*$-algebra has a quasi-representation into the Banach space $\mathbb{B}(\mathscr{H},\mathscr{K})$ of all bounded linear operators between some Hilbert spaces $\mathscr{H}$ and $\mathscr{K}$. We define the notion of completely positive $\varphi$-morphism and establish a Stinespring type theorem in the framework of Finsler modules over $C^*$-algebras. We also investigate the nondegeneracy and the irreducibility of quasi-representations.