GROWTH CONDITIONS AND INVERSE PRODUCING EXTENSIONS

Catalin Badea (1, 2) , Vladimir Müller

1 Université de Lille
2 LPP - Laboratoire Paul Painlevé - UMR 8524

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 (β). Other applications are also given.

Domaines: Analyse fonctionnelle [math.FA]

Catalin Badea, Vladimir Müller. GROWTH CONDITIONS AND INVERSE PRODUCING EXTENSIONS. J. Operator Th., 2005, 54 (2), pp.415-439. ⟨hal-03494698⟩