Growth conditions and inverse producing extensions

Details Growth conditions and inverse producing extensions Growth conditions and inverse producing extensions

2005-12-14

arxiv.org/abs/math/0512321v1

Mathematics

Functional Analysis

22 pages

Scientific paper

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.

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