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Journal of Operator Theory

Volume 70, Issue 1, Summer 2013  pp. 75-107.

Regularity criteria for Banach function algebras

Authors Ernst Albrecht (1) and Tazeen Athar (2)
Author institution: (1) Fachrichtung 6.1 - Mathematik, Universitaet des Saarlandes, 66041 Saarbrucken, Germany
(2) Department of Mathematics, Comsats Institute of Information Technology, Islamabad, Pakistan

Summary:  By means of a variant of a theorem of Yngve Domar we obtain decomposability criteria for bounded linear operators on Banach spaces depending on local growth conditions of the resolvent and local dimension properties of the spectrum. These criteria are then applied to obtain normality and regularity criteria for Banach function algebras of complex ultradifferentiable functions on perfect, compact subsets of the complex plane.

Keywords:  Banach function algebras, decomposable operators

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