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Spectral and asymptotic properties of dominated operators

Part of: General theory of linear operators Special classes of linear operators

Published online by Cambridge University Press:  09 April 2009

Frank Räbiger  and
Manfred P. H. Wolff
Frank Räbiger
Affiliation:
Mathematisches Institut Universität TübingenAuf der Morgenstelle 10 D-72076 TübingenGermanyfrra@michelangelo.mathematik.uni-tuebingen.de manfred.wolff@uni-tuebingen.de
Manfred P. H. Wolff
Affiliation:
Mathematisches Institut Universität TübingenAuf der Morgenstelle 10 D-72076 TübingenGermanyfrra@michelangelo.mathematik.uni-tuebingen.de manfred.wolff@uni-tuebingen.de
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Abstract

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We investigate the relationship between the peripheral spectrum of a positive operator T on a Banach lattice E and the peripheral spectrum of the operators S dominated by T, that is, ]Sx] ≤ T]x] for all x ε E. This can be applied to obtain inheritance results for asymptotic properties of dominated operators.

Keywords

Banach latticedominated operatorsperipheral spectrumessential spectrumalmost periodicityuniform ergodicity.

MSC classification

Secondary: 47B65: Positive operators and order-bounded operators 47A10: Spectrum, resolvent 47A35: Ergodic theory 47A53: (Semi-) Fredholm operators; index theories
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 63 , Issue 1 , August 1997 , pp. 16 - 31
Copyright
Copyright © Australian Mathematical Society 1997

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