The Product Spaces And Norm In-Equalities On The Noncommutative Lorentz Space

In this thesis,our aim is to generalize some result of the classical Lorentz space to the noncommutative Lorentz space in the case that von Neumann algebra has no minimum projection.First,we discuss the boundedness and compactness of left multiplier operators in noncommutative Lorentz spaces by using the relationship between the generalized singular values,the distribution function and the spectral projection of τ-measurable operators,according to the theory of noncommutative Lorentz spaces,some conclusion about the multiplier space of the classical Lorentz space are extended to the noncommutative Lorentz space.Then,by using the definitions and properties of the generalized singular values of the τ-measurable operator we extended the logarithmic submajorisation inequalities of the operator concave function.Finally,we give some inequalities of the 2 × 2 operator matrix.