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arXiv · 0804.1388

Topological Stable Rank of Nest Algebras

Kenneth R. Davidson·You Qing Ji
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Abstract

We establish a general result about extending a right invertible row over a Banach algebra to an invertible matrix. This is applied to the computation of right topological stable rank of a split exact sequence. We also introduce a quantitative measure of stable rank. These results are applied to compute the right (left) topological stable rank for all nest algebras. This value is either 2 or infinity, and rtsr(T(N)) = 2 occurs only when N is of ordinal type less than omega^2 and the dimensions of the atoms grows sufficiently quickly. We introduce general results on `partial matrix algebras' over a Banach algebra. This is used to obtain an inequality akin to Rieffel's formula for matrix algebras over a Banach algebra. This is used to give further insight into the nest case.

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Kenneth R. Davidson, You Qing Ji. 2008-04-09. Topological Stable Rank of Nest Algebras. https://doi.org/10.1112/plms%2Fpdn048

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