首页|THREE KINDS OF DENTABILITIES IN BANACH SPACES AND THEIR APPLICATIONS

THREE KINDS OF DENTABILITIES IN BANACH SPACES AND THEIR APPLICATIONS

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In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak*-weak denting point and the weak*-weak*denting point of a set.These are the generalizations of the weak*denting point of a set in a dual Banach space.By use of the weak*-weak denting point,we characterize the very smooth space,the point of weak*-weak continuity,and the extreme point of a unit ball in a dual Banach space.Meanwhile,we also characterize an approximatively weak compact Chebyshev set in dual Banach spaces.Moreover,we define the nearly weak dentability in Banach spaces,which is a generalization of near dentability.We prove the necessary and sufficient conditions of the reflexivity by nearly weak dentability.We also obtain that nearly weak dentability is equivalent to both the approximatively weak compactness of Banach spaces and the w-strong proximinality of every closed convex subset of Banach spaces.

weak*-weak denting pointnearly weak dentabilityvery smooth spacepoint of weak*-weak continuityextreme pointapproximatively weak compactnessw-strong proximinalityreflexivity

张子厚、周晶

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School of Mathematics,Physics and Statistics,Shanghai University of Engineering Science,Shanghai 201620,China

National Natural Science Foundation of ChinaNatural Science Foundation of Shanghai

1227134423ZR1425800

2024

10.1007/s10473-024-0204-1

数学物理学报(英文版)
中科院武汉物理与数学研究所

数学物理学报(英文版)

CSTPCD
影响因子：0.256
ISSN：0252-9602
年,卷(期)：2024.44(2)
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