Riesz Angles In Orlicz-Lorentz Sequence Spaces

The qualitative geometry property of Orlicz-Lorentz space has been concerned by many scholars. However, few achievements about quantitative geometry properties (geometric constants) were obtained on comparison of the classical Orlicz spaces due to the difficulties from the rearrangements. So it is meaningful to explore the Riesz angles of Orlicz-Lorentz sequence spaces. It can provide a framework for the research of quantitative properties. We discussed the upper and lower bounds of Riesz angles in Orlicz-Lorentz sequence spaces equipped with both the Luxemburg norm and the Orlicz norm. We showed that the Riesz angle ofλΦ,ωandλΦ,ωsatisfies This result generalizes the related research results of Ren Zhongdao. As corollary(1) the Riesz angle of Lorentz spaceλΦ,ωis 2(?)/p;(2)α(λΦ,ω)<2 if and only ifΦ∈▽2(0), if and only ifα(λΦ,ω0)<2.This paper has three chapters,the main results of the thesis are summarized as following:Chapter one:In this chapter, the basical definitions, marks and necessary lemmas are introduced.Chapter two:In this chapter, we discuss the upper and lower bounds of Riesz angles in Orlicz-Lorentz sequence spaces equipped with the Luxemburg norm, figure out the reasonable extent of Riesz angles in the space generated by some N-functions and weight sequence.Chapter three:In this chapter,we estimate the extent of Riesz angles in Orlicz-Lorentz sequence spaces equipped with the Orlicz norm. Through the remark and corollaries,the expressions we deduced are useful.