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

Abramovich, Y. A.; Aliprantis, C. D.; Burkinshaw, O.

doi:10.1090/S0002-9939-1995-1242069-9

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

Proc. Amer. Math. Soc. 123 (1995), 1773-1777

DOI: https://doi.org/10.1090/S0002-9939-1995-1242069-9

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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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