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

DOI:
https://doi.org/10.1090/S0002-9939-97-03885-9

MathSciNet review:
1396983

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-97-03885-9

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