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Spectral and asymptotic properties of resolvent-dominated operators

Part of: General theory of linear operators Special classes of linear operators Groups and semigroups of linear operators, their generalizations and applications

Published online by Cambridge University Press:  09 April 2009

Frank Räbiger  and
Manfred P. H. Wolff
Manfred P. H. Wolff
Affiliation:
Mathematisches Institut Universität Tübigen Auf der Morgenstelle 10 D-72076 Tübingen Germany e-mail: frra@michelangelo.mathematik.uni-tuebingen.de e-mail: manfred.wolff@uni-tuebingen.de
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Abstract

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Let A and B be (not necessarily bounded) linear operators on a Banach lattice E such that |(s – B)-1x|≤ (s – A)-1|x| for all x in E and sufficiently large s ∈ R. The main purpose of this paper is to investigate the relation between the spectra σ(B) and σ(A) of B and A, respectively. We apply our results to study asymptotic properties of dominated C0-semigroups.

Keywords

Banach latticedominated pseudo-resolventsdominated C0-semigroupsperipheral spectrumessential spectrumalmost periodicityuniform ergodicity.

MSC classification

Secondary: 47A10: Spectrum, resolvent 47B65: Positive operators and order-bounded operators 47D03: Groups and semigroups of linear operators
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 2 , April 2000 , pp. 181 - 201
Copyright
Copyright © Australian Mathematical Society 2000

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