- Turkish Journal of Mathematics
- Vol: 35 Issue: 2
- Invariant subspace problem for positive L-weakly and M-weakly compact operators
Invariant subspace problem for positive L-weakly and M-weakly compact operators
Authors : Cevriye Tonyali, Erdal Bayram
Pages : 267-273
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Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :In this paper, we show that positive L-weakly and M-weakly compact operators on some real Banach lattices have a non-trivial closed invariant subspace. Also, we prove that any positive L-weakly (or M-weakly) compact operator T:E \rightarrow E\ has a non-trivial closed invariant subspace if there exists a Dunford-Pettis operator S:E \rightarrow E satisfying 0 \leq T \leq S, where E is Banach lattice.Keywords : Invariant subspace, L- and M-weakly compact operator, Polynomially L-weakly (M-weakly) compact operator, Dunford-Pettis operator