On the Bound of the C* Exponential Length. Issue 4 (1st December 2014)

• Record Type: Journal Article
• Authors: Pan, Qingfei; Wang, Kun
• Is Part Of: Canadian mathematical bulletin =. Volume 57:Issue 4(2014)
• Page Start: 853
• Page End: 869
• Publication Date: 2014-12-01
• Subjects: 46L05; exponential length; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/CMB-2014-044-8
• Languages: English
• ISSNs: 0008-4395

Abstract

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 $\pi$ . Moreover, in simple inductive limit ${{C}^{*}}$ -algebras, similar examples also exist.