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

 Printed: Dec 2014
  • Qingfei Pan,
    School of Mechanical and Electrical Engineering, Sanming University, Sanming, Fujian, China
  • Kun Wang,
    Department of Mathematics, University of Puerto Rico, Rio Piedras Campus, San Juan, Puerto Rico, USA 00931
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Let $X$ be a compact Hausdorff space. In this paper, we give an example to show that there is $u\in \mathrm{C}(X)\otimes \mathrm{M}_n$ with $\det (u(x))=1$ for all $x\in X$ and $u\sim_h 1$ 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.
Keywords: exponential length exponential length
MSC Classifications: 46L05 show english descriptions General theory of $C^*$-algebras 46L05 - General theory of $C^*$-algebras

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