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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Invariant subspaces for positive operators acting on a Banach space with basis
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by Y. A. Abramovich, C. D. Aliprantis and O. Burkinshaw PDF
Proc. Amer. Math. Soc. 123 (1995), 1773-1777 Request permission

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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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 1773-1777
  • MSC: Primary 47A15; Secondary 47B65
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1242069-9
  • MathSciNet review: 1242069