On the topological stable rank of non-selfadjoint operator algebras |
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Authors: | K R Davidson R H Levene L W Marcoux H Radjavi |
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Institution: | (1) Department of Pure Mathematics, University of Waterloo, Waterloo, ON, Canada, N2L 3G1;(2) Department of Pure Mathematics, Queen’s University Belfast, Belfast, BT7 1NN, Northern Ireland, UK |
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Abstract: | We provide a negative solution to a question of M. Rieffel who asked if the right and left topological stable ranks of a Banach
algebra must always agree. Our example is found amongst a class of nest algebras. We show that for many other nest algebras,
both the left and right topological stable ranks are infinite. We extend this latter result to Popescu’s non-commutative disc
algebras and to free semigroup algebras as well.
K. R. Davidson, L. W. Marcoux, H. Radjavi’s research was supported in part by NSERC (Canada).
An erratum to this article can be found at |
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Keywords: | 47A35 47L75 19B10 |
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