Some Inequalities About Cartesian Decomposities In Noncommutative Lp-spaces

This paper contains two chapters, the outline of the paper is arranged as follows:Chapter 1 mainly introduces some notations, definitions and some properties of operator.In chapter 2, using the properties of singular values ofτ-measurable operators, convex function and concave function, we generalize the results on matrices in [1] to the case of theτ-measurable operators. It contains two main results as bellow:(a) Let A, B be Self-adjoint operators and letτ-measurable operator T = A + iB. Then For 2≤p≤∞, we haveand for 1≤p≤2, we have(b) For 2≤p≤∞, we haveand for 1≤p≤2, we have...