Topological Free Entropy Dimensions in Nuclear C$^*$-algebras and in Full Free Products of C$^*$-algebras

Details Topological Free Entropy Dimensions in Nuclear C$^*$-algebras and in Full Free Products of C$^*$-algebras Topological Free Entropy Dimensions in Nuclear C$^*$-algebras and in Full Free Products of C$^*$-algebras

2008-02-03

arxiv.org/abs/0802.0281v4

Mathematics

Operator Algebras

Scientific paper

In the paper, we introduce a new concept of topological orbit dimension of $n$-tuples of elements in a unital C$^*$ 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$^*$ 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$^*$ algebras. In the appendix, we show that unital full free product of Blackadar and Kirchberg's unital MF algebras is also MF algebra.

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