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Spectral synthesis and applications to C0-groups

Part of: Groups and semigroups of linear operators, their generalizations and applications

Published online by Cambridge University Press:  09 April 2009

M. Zarrabi
M. Zarrabi
Affiliation:
U.F.R de Mathématiques et InformatiqueUniversité BordeauxI 351, cours de la Liberation 33405 TalenceFrance e-mail: zarrabi@math.u-bordeaux.fr
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Abstract

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Let k ≥ 0 be an integer, T = (T(t))t ∈R a C0-group of bounded operators and A the infinitesimal generator of T. We prove that if, and , and if the spectrum of A is equal to {λ}, then A is bounded and (A – λ)k+1 = 0. Examples are given to show that these conditions are, essentially, the best possible.

MSC classification

Secondary: 47D03: Groups and semigroups of linear operators
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 60 , Issue 1 , February 1996 , pp. 128 - 142
Copyright
Copyright © Australian Mathematical Society 1996

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