Geodesic
On the Bound of the C* Exponential Length
Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 853-869

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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.
DOI : 10.4153/CMB-2014-044-8
Mots-clés : 46L05, exponential length 
Pan, Qingfei; Wang, Kun. On the Bound of the C* Exponential Length. Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 853-869. doi: 10.4153/CMB-2014-044-8
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     title = {On the {Bound} of the {C*} {Exponential} {Length}},
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     pages = {853--869},
     year = {2014},
     volume = {57},
     number = {4},
     doi = {10.4153/CMB-2014-044-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-044-8/}
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