Topological Stable Rank of Nest Algebras
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.
Keywords
Cite
@article{arxiv.0804.1388,
title = {Topological Stable Rank of Nest Algebras},
author = {Kenneth R. Davidson and You Qing Ji},
journal= {arXiv preprint arXiv:0804.1388},
year = {2014}
}