Invariant subspace problem for positive L-weakly and M-weakly compact operators

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.

Anahtar Kelimeler:

Invariant subspace, L- and M-weakly compact operator, Polynomially L-weakly (M-weakly) compact operator, Dunford-Pettis operator

Invariant subspace problem for positive L-weakly and M-weakly compact operators

Keywords:

Invariant subspace, L- and M-weakly compact operator, Polynomially L-weakly (M-weakly) compact operator, Dunford-Pettis operator,

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Cevriye TONYALI, Erdal BAYRAM Department of Mathematics Faculty of Science and Arts, Gazi Universty Ankara-TURKEY e-mail: bayramer@gmail.com