Matricial topological ranks for two algebras of bounded holomorphic functions

Mortini, Raymond, Rupp, Rudolf and Sasane, Amol J. ORCID: 0000-0001-5566-9877 (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
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	28 Jul 2011 09:24
Last Modified:	01 Oct 2024 03:37
URI:	http://eprints.lse.ac.uk/id/eprint/37647

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