Mazur intersection property for Asplund spaces

弱Asplund空间与一维空间的乘积仍为弱Asplund空间：历时45年的开放问题获解

The product of a weak Asplund space and a one-dimensional space is a weak Asplund space: over 45 years of open problem solved

该研究证明弱Asplund空间与一维空间的乘积仍为弱Asplund空间，结合博弈论、极大单调算子等方法，历时45年解决了Larman与Phelps提出的开放问题。

On uniform Mazur intersection property

In this paper, we show that a Banach space $X$ has the Uniform Mazur Intersection Property (UMIP) if and only if every $f \in S(X^*)$ is uniformly w*-semidenting point of $B(X^*)$. We also prove analogous results for uniform w*-MIP.

关于弱Asplund局部凸空间的乘积

On the product of Weak Asplund locally convex spaces

本研究系统梳理局部凸空间中可微空间与Asplund类空间的等价定义，推广Mazur定理得到可分Baire局部凸空间与可分Fréchet空间族乘积为弱Asplund空间，并证明Banach空间族乘积及Σ-乘积的Asplund性质等价于各因子空间的Asplund性质。

关于继承性Mazur交集性质的简短说明

A short note on hereditary Mazur intersection property

本文通过Borwein和Fabian的例子证明继承性Mazur交集性质不蕴含弗雷歇平滑性。

The Mazur Intersection Property and Farthest Points

K.\ S.\ Lau had shown that a reflexive Banach space has the Mazur Intersection Property (MIP) if and only if every closed bounded convex set is the closed convex hull of its farthest points. In this work, we show that in general this latter property is equivalent to a property stronger than the MIP. As corollaries, we recapture the result of Lau and characterize the w*-MIP in dual of RNP spaces.

Extreme contractions in ${\cal L}(\ell^p_2, \ell^q_2)$ and the mazur intersection property in $\ell^p_2 \otimes_{\p} \ell^q_2$

In this paper, we show that the projective tensor product of a two-dimen\-sional $\ell^p$ space with a two-dimensional $\ell^q$ space never has the Mazur Intersection Property for a large range of values of $p$ and $q$. For this purpose, we characterise the extreme contractions from $\ell^p_2$ to $\ell^q_2$ and obtain their closure.