Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A15, 47B65

Retrieve articles in all journals with MSC: 47A15, 47B65

Additional Information

Article copyright: © Copyright 1995 American Mathematical Society