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Journal of Operator Theory

Volume 46, Issue 2, Fall 2001  pp. 221-250.

Normality, non-quasianalyticity and invariant subspaces

Authors K. Kellay (1), and M. Zarrabi (2)
Author institution: (1) Universite de Provence, CMI-LATP UMR 6632, no. 39, rue F. Joliot-Curie, 13453 Marseille Cedex 13, France
(2) Universite Bordeaux I, 351, cours de la Liberation, 33405 Talence Cedex, France

Summary:  We prove that some classes of functions, defined on a closed set in the complex plane with planar Lebesgue measure zero, are non-quasiana\-lytic. We particular ly treat the Carleman classes and classes of functions having asymtotically hol omorphic continuation. Combining this with Dyn'kin's functional calculus based on the Cauchy-Pompeiu formula, we establish the existence of invariant subspac es for operators for which a part of the spectrum is of planar Lebesgue measure zero, provided that the resolvent has a moderate growth near this part of the s pectrum.

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