On the constant of Lipschitz approximability

IF 1.2 2区数学 Q1 MATHEMATICS Transactions of the American Mathematical Society Pub Date : 2024-01-03 DOI:10.1090/tran/9110

Rubén Medina

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引用次数: 0

Abstract

In this note we find λ > 1 \lambda >1 and give an explicit construction of a separable Banach space X X such that there is no λ \lambda -Lipschitz retraction from X X onto any compact convex subset of X X whose closed linear span is X X . This is closely related to a well-known open problem raised by Godefroy and Ozawa in 2014 and represents the first known example of a Banach space with such a property.

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关于 Lipschitz 近似性常数

在本论文中，我们找到了 λ > 1 \lambda >1，并给出了可分离巴拿赫空间 X X 的明确构造，即不存在从 X X 到 X X 的任何紧凑凸子集的 λ \lambda -Lipschitz 回缩，而 X X 的闭线性跨度是 X X。这与 Godefroy 和 Ozawa 在 2014 年提出的一个众所周知的开放问题密切相关，是具有这种性质的巴拿赫空间的第一个已知例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.

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