In this article, we prove the following results： （1） A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; （2） A ...In this article, we prove the following results： （1） A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; （2） A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set.展开更多
We express the set of exposed points in terms of rotund points and non-smooth points.As long as we have Banach spaces each time＂bigger＂,we consider sets of non-smooth points each time＂smaller＂.
In this paper, by using the generating function Φ and X the criteria of the rotundity for the Orlicz-Bochner function and sequence spaces endowed with the Luxemburg norm were obtained. And the sufficient and necessar...In this paper, by using the generating function Φ and X the criteria of the rotundity for the Orlicz-Bochner function and sequence spaces endowed with the Luxemburg norm were obtained. And the sufficient and necessary conditions were given for the extreme point of Orlicz-Bochner sequence space and the conditions in part for Orlicz-Bochner function space.展开更多
Three characteristics of the very rotund space ape proved and the relationships between the very rotund space and the geometrical properties of Banach space are discussed. Also connection between the weakly exposed po...Three characteristics of the very rotund space ape proved and the relationships between the very rotund space and the geometrical properties of Banach space are discussed. Also connection between the weakly exposed points and Radon Nikodym-property is established.展开更多
K-UR,K-LUR and K-R are the generalizations of UR,LUR and R respectively,which are of great significance in Banach space theory.While in Orlicz–Lorentz function spaceΛ_(ϕ,ω)^(◦)[0,γ)equipped with the Orlicz norm,th...K-UR,K-LUR and K-R are the generalizations of UR,LUR and R respectively,which are of great significance in Banach space theory.While in Orlicz–Lorentz function spaceΛ_(ϕ,ω)^(◦)[0,γ)equipped with the Orlicz norm,the research methods of K-UR,K-LUR and K-R are much more complicated than those of UR,LUR and R.In this paper we obtain some criteria of K-UR,K-LUR and K-R ofΛ_(ϕ,ω)^(◦)[0,γ)by means of the norm of dual space and H_(μ)property ofΛ_(ϕ,ω)^(◦)[0,γ).展开更多
基金supported by the National Natural Science Foundation of China(11671252)supported by the National Natural Science Foundation of China(11771278)
文摘In this article, we prove the following results： （1） A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; （2） A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set.
文摘We express the set of exposed points in terms of rotund points and non-smooth points.As long as we have Banach spaces each time＂bigger＂,we consider sets of non-smooth points each time＂smaller＂.
文摘In this paper, by using the generating function Φ and X the criteria of the rotundity for the Orlicz-Bochner function and sequence spaces endowed with the Luxemburg norm were obtained. And the sufficient and necessary conditions were given for the extreme point of Orlicz-Bochner sequence space and the conditions in part for Orlicz-Bochner function space.
文摘Three characteristics of the very rotund space ape proved and the relationships between the very rotund space and the geometrical properties of Banach space are discussed. Also connection between the weakly exposed points and Radon Nikodym-property is established.
基金Supported by NSFC(Grant No.11771273)National Science Research Project of Anhui Educational Department(Grant No.KJ2019A0487)。
文摘K-UR,K-LUR and K-R are the generalizations of UR,LUR and R respectively,which are of great significance in Banach space theory.While in Orlicz–Lorentz function spaceΛ_(ϕ,ω)^(◦)[0,γ)equipped with the Orlicz norm,the research methods of K-UR,K-LUR and K-R are much more complicated than those of UR,LUR and R.In this paper we obtain some criteria of K-UR,K-LUR and K-R ofΛ_(ϕ,ω)^(◦)[0,γ)by means of the norm of dual space and H_(μ)property ofΛ_(ϕ,ω)^(◦)[0,γ).
