On the Bound of the C* Exponential Length. Issue 4 (1st December 2014) - Pan, Qingfei; Wang, Kun
Abstract: Let $X$ be a compact Hausdorff space. In this paper, we give an example to show that there is $u\, \in \, C\left( X \right)\, \otimes \, {M_{n}}$ with $\det \left( u\left( x \right) \right)\, =\, 1$ for all $x\, \in \, X$ and $u{{\tilde{\ }}_{h}}1$ such that the ${C^{*}}$ exponential length of $u$ (denoted by $\text{cel}\left( u \right)$ ) cannot be controlled by $π$ . Moreover, in simple inductive limit ${C^{*}}$ -algebras, similar examples also exist.