On the Bound of the $mathrm{C}^*$ Exponential Length

Canadian mathematical bulletin

Kun Wang¹  Qingfei Pan² 

[1] Department of Mathematics, University of Puerto Rico, Rio Piedras Campus, San Juan, Puerto Rico, USA 00931;School of Mechanical and Electrical Engineering, Sanming University, Sanming, Fujian, China

关键词: exponential length;   

DOI  :  10.4153/CMB-2014-044-8

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $X$ be a compact Hausdorff space. In this paper, we give anexample to show that there is $uin mathrm{C}(X)otimes mathrm{M}_n$with $det (u(x))=1$ for all $xin X$ and $usim_h 1$ such that the$mathrm{C}^*$ exponential length of $u$ (denoted by $cel(u)$) can not be controlled by$pi$. Moreover, in simple inductive limit $mathrm{C}^*$-algebras,similar examples also exist.

【 授权许可】

Unknown