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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the ideal-triangularizability
of positive operators on Banach lattices


Author: Mohammed Taghi Jahandideh
Journal: Proc. Amer. Math. Soc. 125 (1997), 2661-2670
MSC (1991): Primary 47B65, 47A15
MathSciNet review: 1396983
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Abstract: There are some known results that guarantee the existence of a nontrivial closed invariant ideal for a quasinilpotent positive operator on an $AM$-space with unit or a Banach lattice whose positive cone contains an extreme ray. Some recent results also guarantee the existence of such ideals for certain positive operators, e.g. a compact quasinilpotent positive operator, on an arbitrary Banach lattice. The main object of this article is to use these results in constructing a maximal closed ideal chain, each of whose members is invariant under a certain collection of operators that are related to compact positive operators, or to quasinilpotent positive operators.


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Additional Information

Mohammed Taghi Jahandideh
Affiliation: Department of Mathematics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5
Address at time of publication: School of Mathematics, Isfahan University of Technology, Isfahan 84156, Iran

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03885-9
PII: S 0002-9939(97)03885-9
Received by editor(s): December 11, 1995
Received by editor(s) in revised form: March 29, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society