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.
Invariant subspace, L- and M-weakly compact operator, Polynomially L-weakly (M-weakly) compact operator, Dunford-Pettis operator
TONYALI, CEVRİYE and BAYRAM, ERDAL
"Invariant subspace problem for positive L-weakly and M-weakly compact operators,"
Turkish Journal of Mathematics: Vol. 35:
2, Article 8.
Available at: https://journals.tubitak.gov.tr/math/vol35/iss2/8