Topological free entropy dimension in unital C~*-algebras

摘要

The notion of topological free entropy dimension of n-tuple of elements in a unital C~* algebra was introduced by Voiculescu. In the paper, we compute topological free entropy dimension of one self-adjoint element and topological free orbit dimension of one self-adjoint element in a unital C~* algebra. We also calculate the values of topological free entropy dimensions of any families of self-adjoint generators of some unital C~* algebras, including irrational rotation C~* algebra, UHF algebra, and minimal tensor product of two reduced C~* algebras of free groups.