Some Geometric Constants Of Noncommutative Orlicz Spaces

Noncommutative Orlicz spaces are the generalization of noncommutative Lp spaces.It is widely used in the fields of quantum physics,quantum information and quantum computing,non commutative harmonic analysis and so on.In 1990,Kunze gave the definition of noncommutative Orlicz space in algebraic form for the first time.Since then,mathematicians have carried out a series of research work on noncommutative Orlicz space.The geometric constants of spaces are common ways to characterize the geometric properties.The geometric constants of Banach spaces can express their geometric properties intuitively and effectively.Besides,there are usually many connections among constants.Even some constants have equivalence relations,which can be flexibly used to solve various problems.In this paper,some modulus and constants in noncommutative Orlicz space equipped with the Luxemburg norm and the Orlicz norm are discussed firstly.The upper monotone coefficients of these spaces and a point of their unit sphere are computed.When a(?)>0,the lower monotone modulus of noncommutative Orlicz spaces equipped with the Luxemburg norm are given.Furthermore,the criteria for uniform monotonicity and strict monotonicity of noncommutative Orlicz space are obtained.Secondly,the modulus of convexity and the coefficient of convexity of noncommutative Orlicz space equipped with the Luxemburg norm are discussed.Furthermore,the judgment condition of uniform convexity of noncommutative Orlicz space is obtained.