Finite approximation properties of $C^{*}$-modules II

TL;DR

This paper investigates the properties of $C^*$-modules, focusing on quasidiagonality, local reflexivity, and a new notion of amenability for vector-valued traces, expanding understanding of $C^*$-algebra structures.

Contribution

It introduces and analyzes a novel concept of amenability for vector-valued traces within the context of $C^*$-modules, advancing the theory of $C^*$-algebra properties.

Findings

Established conditions for quasidiagonality in $C^*$-modules.

Characterized local reflexivity for $C^*$-algebras with compatible actions.

Proposed a new framework for amenability of vector-valued traces.

Abstract

We study quasidiagonality and local reflexivity for $C^{*}$-algebras which are $C^*$-module over another $C^*$-algebra with compatible actions. We introduce and study a notion of amenability for vector valued traces.