从最佳协同逼近的角度看巴拿赫空间的某些特殊子空间

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引用次数: 0

摘要

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

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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