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On the Bound of the C* Exponential Length
Published online by Cambridge University Press: 20 November 2018
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.
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- Copyright © Canadian Mathematical Society 2014