Some Results on Matricial Field C-Algebras

TL;DR

This paper explores properties of MF algebras, extending existing theorems, introducing a new class called AM algebras, and examining the relationship between real and complex C-algebras.

Contribution

It generalizes Voiculescu's Representation Theorem for certain MF algebras and introduces the concept of AM algebras, expanding the understanding of MF algebra structures.

Findings

Inner quasidiagonal C-algebras are MF algebras

A real C-algebra is MF iff its complexification is MF

Introduces and studies properties of AM algebras

Abstract

In this paper, we consider Blackadar and Kirchberg's MF algebras. We show that any inner quasidiagonal C-algebra is MF algebra and we generalize Voiculescu's Representation Theorem for a special version of MF algebras. Moreover, we define a weak version of MF algebras namely matrical amenable (AM) algebras, and prove some results related to this new notion. Finally, we consider real C-algebras and we show that a real C-algebra is MF if and only if its complexification is MF.