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Journal of Operator Theory

Volume 54, Issue 2, Fall 2005  pp. 415-439.

Growth conditions and inverse producing extensions

Authors Catalin Badea (1) and Vladimir Mueller (2)
Author institution: (1) D\'epartement de Math\'ematiques, UMR CNRS no. 8524, Universit\'e Lille I, F-59655 Villeneuve d'Ascq, France, (2) Institut of Mathematics AV CR, Zitna 25, 115 67 Prague 1, Czech Republic

Summary:  We study the invertibility of Banach algebras elements in their extensions, and invertible extensions of Banach and Hilbert space operators with prescribed growth conditions for the norm of inverses. As applications, the solutions of two open problems are obtained. In the first one we give a characterization of $\et$-subscalar operators in terms of growth conditions. In the second one we show that operators satisfying a Beurling-type growth condition possess Bishop's property $(\beta)$. Other applications are also given.

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