Research On Non-commutative Orlicz Spaces

This thesis is devoted to study the noncommutative Orlicz spaces and which is divided into four sections and stated as follows:In the first section, we give the research status and present some notations together with definitions.In section two, we consider the relationships of growth functions and some properties of the functions, some basic results of noncommutative Orlicz spaces associated with growth functions and N-functions, the Szeg¨o and Riesz type factorization theorems of noncommutative Orlicz-Hardy spaces and inner-outer factorizations for noncommutative Orlicz-Hardy spaces.In section three, we proved contractivity of conditional expectation E and tracial subalgebra A of M has LΦ-factorization if and only if A is a subdiagonal algebra. We also give some characterizations of subdiagonal algebras.In section four, we study the noncommutative Orlicz modular spaces associated with growth functions. We prove dominated convergence theorems, Young inequalities and ClarksonMc Carthy inequalities for this spaces.