On some special subspaces of a Banach space, from the perspective of best coapproximation

Monatshefte für Mathematik Pub Date : 2024-01-23 DOI:10.1007/s00605-023-01930-2

引用次数: 0

Abstract

We study the best coapproximation problem in Banach spaces, by using Birkhoff–James orthogonality techniques. We introduce two special types of subspaces, christened the anti-coproximinal subspaces and the strongly anti-coproximinal subspaces. We obtain a necessary condition for the strongly anti-coproximinal subspaces in a reflexive Banach space whose dual space satisfies the Kadets–Klee Property. On the other hand, we provide a sufficient condition for the strongly anti-coproximinal subspaces in a general Banach space. We also characterize the anti-coproximinal subspaces of a smooth Banach space. Further, we study these special subspaces in a finite-dimensional polyhedral Banach space and find some interesting geometric structures associated with them.

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从最佳协同逼近的角度看巴拿赫空间的某些特殊子空间

摘要我们利用伯克霍夫-詹姆斯正交技术研究巴拿赫空间中的最佳逼近问题。我们引入了两种特殊类型的子空间，分别称为反逼近子空间和强反逼近子空间。我们得到了反向巴拿赫空间中强反oproximinal子空间的必要条件，其对偶空间满足卡德茨-克利性质（Kadets-Klee Property）。另一方面，我们为一般巴拿赫空间中的强反oproximinal子空间提供了一个充分条件。我们还描述了光滑巴拿赫空间的反oproximinal子空间的特征。此外，我们还研究了有限维多面体巴拿赫空间中的这些特殊子空间，并发现了与之相关的一些有趣的几何结构。

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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Monatshefte für Mathematik

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