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Matricial topological ranks for two algebras of bounded holomorphic functions

Mortini, Raymond, Rupp, Rudolf and Sasane, Amol J. (2010) Matricial topological ranks for two algebras of bounded holomorphic functions. Linear and Multilinear Algebra, 58 (6). pp. 741-752. ISSN 0308-1087

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Abstract

Let N and D be two matrices over the algebra H ∞ of bounded analytic functions in the disk, or its real counterpart . Suppose that N and D have the same number n of columns. In a generalization of the notion of topological stable rank 2, it is shown that N and D can be approximated (in the operator norm) by two matrices Ñ and , so that the Aryabhatta–Bezout equation admits a solution. This has particular interesting consequences in systems theory. Moreover, in case that N is a square matrix, X can be chosen to be invertible in the case of the algebra H ∞, but not always in the case of .

Item Type: Article
Official URL: http://www.tandf.co.uk/journals/LAMA
Additional Information: © 2010 Taylor & Francis
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 28 Jul 2011 09:24
URL: http://eprints.lse.ac.uk/37647/

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