MF-traces and a Lower Bound for the Topological Free Entropy Dimension in Unital C*-algebras
Don Hadwin, Qihui Li, Weihua Li, Junhao Shen
TL;DR
This paper advances the understanding of Voiculescu's topological free entropy dimension in unital C*-algebras by introducing MF-traces and related concepts to establish bounds and exact formulas for { extdelta}_{top}.
Contribution
It introduces MF-trace, MF-ideal, and MF-nuclearity concepts to derive bounds and exact values for the topological free entropy dimension.
Findings
Established upper and lower bounds for { extdelta}_{top}
Derived exact formulas for { extdelta}_{top} in many cases
Discussed semicontinuity properties of { extdelta}_{top}
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}.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Random Matrices and Applications · Algebraic structures and combinatorial models