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.
Invariant subspace, L-weakly compact operator, M-weakly compact operator, quasi-similarity
"Invariant subspaces of operators quasi-similar to L-weakly and M-weaklycompact operators,"
Turkish Journal of Mathematics: Vol. 42:
1, Article 12.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss1/12