首页/论文/2012.12538

arXiv 2012.125382020-12-23math.FA

On uniform Mazur intersection property

Pradipta Bandyopadhyay, Jadav Ganesh, Deepak Gothwal

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

关于继承性Mazur交集性质的简短说明

A short note on hereditary Mazur intersection property

Stat–Math Division, Indian Statistical Institute（印度统计学院统计学与数学系）；Department of Mathematics, Indian Institue of Technology, Kharagpur（印度理工学院卡拉格普尔分校数学系）

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。

2026-02-19math.FA

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.

1994-12-22math.FA

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.

1994-12-12math.FA

Mazur intersection property for Asplund spaces

The main result of the present note states that it is consistent with the ZFC axioms of set theory (relying on Martin's Maximum MM axiom), that every Asplund space of density character $ω_1$ has a renorming with the Mazur intersection property. Combined with the previous result of Jim\' enez and Moreno (based upon the work of Kunen under the continuum hypothesis) we obtain that the MIP normability of Asplund spaces of density $ω_1$ is undecidable in ZFC.

2008-04-03math.FA

The Generalised (Uniform) Mazur Intersection Property

Given a family $\mathcal{C}$ of closed bounded convex sets in a Banach space $X$, we say that $X$ has the $\mathcal{C}$-MIP if every $C \in \mathcal{C}$ is the intersection of the closed balls containing it. In this paper, we introduce a stronger version of the $\mathcal{C}$-MIP and show that it is a more satisfactory generalisation of the MIP inasmuch as one can obtain complete analogues of various characterisations of the MIP. We also introduce uniform versions of the (strong) $\mathcal{C}$-MIP and characterise them analogously. Even in this case, the strong $\mathcal{C}$-UMIP appears to hav…

2023-01-05math.FA

更多相关论文收起更多论文

The Mazur-Ulam property for uniform algebras

We give a sufficient condition for a Banach space with which the homogeneous extension of a surjective isometry from the unit sphere of it onto another one is real-linear. The condition is satisfied by a uniform algebra and a certain extremely $C$-regular space of real-valued continuous functions.

2021-07-04math.FA

The Mazur-Ulam property for a Banach space which satisfies a separation condition

We study $C$-rich spaces, lush spaces, and $C$-extremely regular spaces concerning with the Mazur-Ulam property. We show that a uniform algebra and the real part of a uniform algebra with the supremum norm are $C$-rich spaces, hence lush spaces. We prove that a uniformly closed subalgebra of the algebra of complex-valued continuous functions on a locally compact Hausdorff space which vanish at infinity is $C$-extremely regular provided that it separates the points of the underlying space and has no common zeros. In section 3 we exhibit descriptions on the Choquet bounday, the \vSilov bounday, …

2022-05-04math.FA

酉不变理想球面之间的均匀同胚

Uniform homeomorphisms between spheres of unitarily invariant ideals

本文证明非交换版本的Odell-Schlumprecht定理，通过两类广义Mazur映射（基于p-凸化和量子相对熵最小化）建立酉不变理想球面与Hilbert空间球面间的均匀同胚，提供满足性质(H)的新例子。

2023-05-11math.FAmath.OA

非一致连续的最近点映射

Non-uniformly continuous nearest point maps

构造一个局部一致凸的Banach空间，其上到任意紧凸子集的最近点映射连续但非一致连续，并证明任意无限维可分Banach空间在Banach-Mazur距离下可任意接近此类空间。

2024-02-07math.FAmath.MG

Polynomial estimates and radius of analyticity on real Banach spaces

A generalization of Problem 73 of Mazur and Orlicz in the Scottish Book was introduced from L. Harris. The exact value of the constant that appears there is known when complex normed linear spaces are considered. In this paper, we give estimates in the case of an arbitrary real normed linear space and a real $\ell_p$ space. Moreover, if $F(x)$ is a power series, $ρ$ its radius of uniform convergence and $ρ_{\substack{A}}$ its radius of analyticity, we prove that $ρ_{\substack{A}}\geqρ/\sqrt{2}$ and give some respective results for the $n$th Fréchet derivative of $F(x)$.

2012-10-29math.FA

Compact Hölder retractions and nearest point maps

In this paper, two main results concerning uniformly continuous retractions are proved. First, an $α$-Hölder retraction from any separable Banach space onto a compact convex subset whose closed linear span is the whole space is constructed for every positive $α<1$. This constitutes a positive solution to a Hölder version of a question raised by Godefroy and Ozawa. In fact, compact convex sets are found to be absolute $α$-Hölder retracts under certain assumption of flatness. Second, we provide an example of a strictly convex Banach space $X$ arbitrarily close to $\ell_2$ (for the Banach Mazur d…

2022-05-25math.FAmath.MG