No CrossRef data available.
Published online by Cambridge University Press: 20 November 2018
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.