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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Communicated by Gerald Teschl.
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S. Sohel and S. Ghosh would like to thank CSIR, Govt. of India, for the financial support in the form of Senior Research Fellowship under the mentorship of Prof. Kallol Paul.
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Sohel, S., Ghosh, S., Sain, D. et al. On some special subspaces of a Banach space, from the perspective of best coapproximation. Monatsh Math 204, 969–987 (2024). https://doi.org/10.1007/s00605-023-01930-2
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DOI: https://doi.org/10.1007/s00605-023-01930-2