关于极值非展开映射

arXiv - MATH - Functional Analysis Pub Date : 2024-09-06 DOI:arxiv-2409.04292

Christian Bargetz, Michael Dymond, Katriin Pirk

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引用次数: 0

摘要

我们研究了有规范空间（其中包括特定的巴拿赫空间）的非空有界封闭凸子集上的无穷映射的极值性。我们发现，对于许多巴拿赫空间，包括具有拉顿-尼科迪姆性质的巴拿赫空间和紧凑豪斯多夫$K的所有$C(K)$空间，外射等距在这个意义上都是极值的。

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On extremal nonexpansive mappings

We study the extremality of nonexpansive mappings on a nonempty bounded closed and convex subset of a normed space (therein specific Banach spaces). We show that surjective isometries are extremal in this sense for many Banach spaces, including Banach spaces with the Radon-Nikodym property and all $C(K)$-spaces for compact Hausdorff $K.$ We also conclude that the typical, in the sense of Baire category, nonexpansive mapping is close to being extremal.

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arXiv - MATH - Functional Analysis

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