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On the Bound of the C* Exponential Length

Published online by Cambridge University Press:  20 November 2018

Qingfei Pan  and
Kun Wang
Qingfei Pan
Affiliation:
School of Mechanical and Electrical Engineering, Sanming University, Sanming, Fujian, China e-mail: pqf101@yahoo.com.cn
Kun Wang
Affiliation:
Department of Mathematics, University of Puerto Rico, Rio Piedras Campus, San Juan, Puerto Rico, USA 00931 e-mail: lingling-1106@hotmail.com
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Abstract

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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.

Keywords

46L05exponential length
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 4 , 01 December 2014 , pp. 853 - 869
Copyright
Copyright © Canadian Mathematical Society 2014

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