Topological Free Entropy Dimensions in Nuclear C${}^{\ast }$-algebras and in Full Free Products of C${}^{\ast }$-algebras

Abstract

In the paper, we introduce a new concept of topological orbit dimension of $n$-tuples of elements in a unital C${}^{\ast }$ algebra. Using this concept, we conclude that the Voiculescu's topological free entropy dimension of any family of self-adjoint generators of a nuclear C${}^{\ast }$ algebra is less than or equal to 1. We also show that the topological free entropy dimension is additive in the full free products of unital C${}^{\ast }$ algebras. In the appendix, we show that unital full free product of Blackadar and Kirchberg's unital MF algebras is also MF algebra.

References in corpus (1)

• Topological Free Entropy Dimension in Unital C^* algebras (II) : Orthogonal Sum of Unital C^*-algebras

Cited by in corpus (1)

• Some Examples of Blackadar and Kirchberg's MF Algebras