Stable Ranks of Banach Algebras of Operator-Valued Analytic Functions |
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Authors: | Amol Sasane |
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Affiliation: | (1) Department of Mathematics, London School of Economics, Houghton Street, London, WC2A 2AE, United Kingdom |
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Abstract: | Let E be a separable infinite-dimensional Hilbert space, and let denote the algebra of all functions that are holomorphic. If is a subalgebra of , then using an algebraic result of Corach and Larotonda, we derive that under some conditions, the Bass stable rank of is infinite. In particular, we deduce that the Bass (and hence topological stable ranks) of the Hardy algebra , the disk algebra and the Wiener algebra are all infinite. Submitted: October 10, 2007., Revised: January 11, 2008., Accepted: January 12, 2007. |
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Keywords: | KeywordHeading" >Mathematics Subject Classification (2000). Primary 30H05 Secondary 47A56, 46J15, 46L80 |
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