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

 

Invariant subspaces for positive operators acting on a Banach space with basis


Authors: Y. A. Abramovich, C. D. Aliprantis and O. Burkinshaw
Journal: Proc. Amer. Math. Soc. 123 (1995), 1773-1777
MSC: Primary 47A15; Secondary 47B65
MathSciNet review: 1242069
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Abstract: Recently we established several invariant subspace theorems for operators acting on an $ {l_p}$-space. In this note we extend these results from operators acting on an $ {l_p}$-space to operators acting on any Banach space with a (not necessarily unconditional) Schauder basis. For instance, it is shown that if a continuous quasinilpotent operator on a Banach space is positive with respect to the closed cone generated by a basis, then the operator has a nontrivial closed invariant subspace.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1242069-9
PII: S 0002-9939(1995)1242069-9
Article copyright: © Copyright 1995 American Mathematical Society