MF-TRACES AND A LOWER BOUND FOR THE TOPOLOGICAL FREE ENTROPY DIMENSION IN UNITAL C*-ALGEBRAS

Abstract

• We continue previous work on Voiculescu's topological free entropy dimension {\delta}_{top}. We introduce the notions of MF-trace, MF-ideal, and MF-nuclearity and use these concepts to obtain upper and lower bounds for {\delta}_{top}, and in many cases we obtain an exact formula for {\delta}_{top}. We also discuss semicontinuity properties of {\delta}_{top}.

• Li, Qihui
• Li, Weihua
• Shen, Junhao

• 2014

Keywords

• C*-algebra
• MF-trace
• Topological free entropy dimension
• free product
• noncommutative continuous function

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