Some Geometric Properties Of Symmetric Spaces Of Measurable Operators

Noncommutative mathematics is a mathematical field parallel with quantum physics,which is the mathematical basis of many physical theories such as quantum statistical physics,quantum field theory,quantum information and quantum com-puting.In this paper,we study the geometric properties of the symmetric spaces of measurable operators,which belong to the category of noncommutative mathemat-ics.The symmetric spaces of measurable operators are related to the semi-finite von Neumann algebra with normal,semi-finite and faithful trace.And the establish-ment of various lifting results which from the symmetric spaces to the symmetric spaces of measurable operators can e?ectively simplify the studies of the geometric structures of the symmetric spaces of measurable operators into the corresponding problems of symmetric spaces.This paper mainly studies the following aspects:Firstly,discussing the inheritance and enhancement of strict monotonicity and local uniform monotonicity from the symmetric function spaces E to the symmetric spaces of measurable operators E(M,?).Secondly,the inheritance and promotion of average local uniform convexity are discussed.Finally,the geometric properties of the unitary matrix spaces C_Eand the symmetric sequence spaces E are studied.Mainly discussing a class of unitary matrix spaces—–noncommutative Orlicz sequence spaces.The characterizations of strict monotone points and local uniform monotone points in the spaces are studied.