This is an announcement for the paper "Growth conditions and inverse producing extensions" by Catalin Badea and Vladimir Mueller.
Abstract: 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 E(T)-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.
Archive classification: Functional Analysis; Operator Algebras
Remarks: 22 pages
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Submitted from: catalin.badea@math.univ-lille1.fr
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