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arXiv · 2407.14471

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

Shamim Sohel·Souvik Ghosh·Debmalya Sain·Kallol Paul
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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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Shamim Sohel, Souvik Ghosh, Debmalya Sain, Kallol Paul. 2024-07-19. On some special subspaces of a Banach space, from the perspective of best coapproximation. https://doi.org/10.1007/s00605-023-01930-2

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