On the Bound of the C* Exponential Length

Abstract

AbstractLet X be a compact Hausdorff space. In this paper, we give an example to show that there is u ∊⊗ C(X) Mn with det(u(x)) = 1 for all x ∊ X and u ~h 1 such that the C* exponential length of u (denoted by ~h cel(u)) cannot be controlled by π. Moreover, in simple inductive limit C*-algebras, similar examples also exist.