Invariant subspaces of operators quasi-similar to L-weakly and M-weakly compact operators


Abstract: Let T be an L-weakly compact operator defined on a Banach lattice E without order continuous norm. We prove that the bounded operator S defined on a Banach space X has a nontrivial closed invariant subspace if there exists an operator in the commutant of S that is quasi-similar to T. Additively, some similar and relevant results are extended to a larger classes of operators called super right-commutant. We also show that quasi-similarity need not preserve L-weakly or M-weakly compactness.

Keywords: Invariant subspace, L-weakly compact operator, M-weakly compact operator, quasi-similarity

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