- Turkish Journal of Mathematics
- Vol: 42 Issue: 1
- Invariant subspaces of operators quasi-similar to L-weakly and M-weakly compact operators
Invariant subspaces of operators quasi-similar to L-weakly and M-weakly compact operators
Authors : Erdal Bayram
Pages : 131-138
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Publication Date : 9999-12-31
Article Type : Makaleler
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