Invariant subspaces of banach lattices

In this thesis work we have studied the following papers by V.G.Troitsky: "On the modulus of CJ.Read' s operator" and "Lomonosov' s theorem cannot be extended to chains of four operators", and by Y.A.Abramovich-C.D.AIiprantis- G.Sirotkin-V.G.Troitsky: "Some open problems and conjuctures associated with the invariant subspace problem". In the above two papers, they have been shown that the modulus of Read' s operator T:ll>lt has an invariant subspace, and there are three operators St, S2 and K such that T commutes with St, St commutes with S2, S2 commutes with K, and K is compact. In the last paper the purpose is to examine two complexification methods of an operator T acting on a real Banach space and present some questions regarding the invariant subspaces of T and those of its complexifications. In the present work, we have collected the necessary definitions and results about the subject. We have given detailed proofs of their theorems. Science Code Key Words Page Number Adviser 403.03.01 Positive operators, Read' s operator, invariant subspaces 74 Associate Professor Çevriye TONY ALI