On the ideal-triangularizability of positive operators on Banach lattices
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- by Mohammed Taghi Jahandideh PDF
- Proc. Amer. Math. Soc. 125 (1997), 2661-2670 Request permission
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.References
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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
- Received by editor(s): December 11, 1995
- Received by editor(s) in revised form: March 29, 1996
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- 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