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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Spectral properties of compact lattice homomorphisms


Author: Anthony W. Wickstead
Journal: Proc. Amer. Math. Soc. 84 (1982), 347-353
MSC: Primary 47B55
DOI: https://doi.org/10.1090/S0002-9939-1982-0640228-8
MathSciNet review: 640228
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Abstract: Given two nonzero eigenvalues of a lattice homomorphism on a relatively uniformly complete vector lattice, of different moduli and with at least one isolated in the set of all eigenvalues, we show that corresponding eigenvectors must be disjoint. The analogous result for the approximate point spectrum of a lattice homomorphism on a Banach lattice is deduced. We give an infinite spectral decomposition for a lattice homomorphism, on a Banach lattice with order continuous norm, which is compact and has an adjoint which is also a lattice homomorphism. From this we deduce that if it has nonnegative spectrum, then it is the direct sum of a nilpotent lattice homomorphism and one that is central.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0640228-8
Article copyright: © Copyright 1982 American Mathematical Society