Topological Stable Rank of Nest Algebras - Mathematics > Operator AlgebrasReport as inadecuate

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Abstract: We establish a general result about extending a right invertible row over aBanach algebra to an invertible matrix. This is applied to the computation ofright topological stable rank of a split exact sequence. We also introduce aquantitative measure of stable rank. These results are applied to compute theright left topological stable rank for all nest algebras. This value iseither 2 or infinity, and rtsrTN = 2 occurs only when N is of ordinal typeless than omega^2 and the dimensions of the atoms grows sufficiently quickly.We introduce general results on `partial matrix algebras- over a Banachalgebra. This is used to obtain an inequality akin to Rieffel-s formula formatrix algebras over a Banach algebra. This is used to give further insightinto the nest case.

Author: Kenneth R. Davidson, You Qing Ji


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