Application Of Interpolation Methods In Noncommutative Orlicz Spaces

This paper contains threes chapters, the outline of the paper is arranged as follows:Chapter 1 presents the background and give out some necessary notations, definitions as well as some properties of operator.In chapter 2, introducing the result on Hardy-Littlewood maximal function of (?)-measurable operators and property of convexΦ-function, then we generalize the conclusions in [1] by replaced p-norm withΦ-norm. It contains two lemma and one theorem as bellow:(a) If (?), we have(b) If for t > 0, we have f_*(|T|)(t) <∞. thenor(c) If T∈L_loc(М; (?)), then there is a constant C > 0, such thatIn these conclusions,Φis a moderate Young convex function, T is a measurable operator.Chapter 3 mainly generalize the conclusions in [2]: Let 1≤p <∞and let T be a sublinear operator acting on L^p(М;(?)) and L^∞(М;(?)). letΦ^-1(u) = u^1/pρ(u^-1/p) for some concave functionρ, we prove that noncommutative Orlicz spaces L_Φ(М) is an interpolation sapce for sublinear operators T between L^p(М;(?)) and L^∞(М;(?)), and...