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On the ideal-triangularizability of positive operators on Banach lattices
Author(s):
Mohammed
Taghi
Jahandideh
Journal:
Proc. Amer. Math. Soc.
125
(1997),
2661-2670.
MSC (1991):
Primary 47B65, 47A15
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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  -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:
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
Copyright of article:
Copyright
1997,
American Mathematical Society
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