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
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.
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).
