Title of article :
Invariant subspace problem for positive L-weakly and M-weakly compact operators
Author/Authors :
Tonyali, Cevriye Gazi Universty - Faculty of Science and Arts - Department of Mathematics, TURKEY , Bayram, Erdal Gazi Universty - Faculty of Science and Arts - Department of Mathematics, TURKEY
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 -- E has a non-trivial closed invariant subspace if there exists a Dunford- Pettis operator S : E -- E satisfying 0 ≤ T ≤ 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.
Journal title :
Turkish Journal of Mathematics
Journal title :
Turkish Journal of Mathematics
