Bayram, Erdal2022-05-112022-05-1120181300-00981303-6149https://doi.org/10.3906/mat-1611-70https://hdl.handle.net/20.500.11776/7429Let 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.en10.3906/mat-1611-70info:eu-repo/semantics/openAccessInvariant subspaceL-weakly compact operatorM-weakly compact operatorquasi-similarityArticle421131138Q3WOS:0004231588000122-s2.0-85040866905Q2