On some subspaces of vector-valued continuous function space, from the perspective of Best coapproximation

Souvik Ghosh; Kallol Paul; Debmalya Sain; Shamim Sohel

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arXiv · 2508.04971

On some subspaces of vector-valued continuous function space, from the perspective of Best coapproximation

Souvik Ghosh·Kallol Paul·Debmalya Sain·Shamim Sohel

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Abstract

This article explores anti-coproximinal and strongly anti-coproximinal subspaces in the spaces of vector-valued continuous functions and operator spaces. We provide a complete characterization of strongly anti-coproximinal subspaces in $ C_0(K, \mathbb{X}) $, under the assumption that the unit ball of $ \mathbb{X}^* $ is the closed convex hull of its weak*-strongly exposed points. Additionally, the work includes a stability analysis of anti-coproximinal and strongly anti-coproximinal subspaces of $ \mathbb{L}(\mathbb{X}, \mathbb{Y}) $ and the space $ \mathbb{Y} $. Beyond these, we present a general characterization of (strong) anti-coproximinal subspaces in the broader context of Banach spaces.

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Souvik Ghosh, Kallol Paul, Debmalya Sain, Shamim Sohel. 2025-08-07. On some subspaces of vector-valued continuous function space, from the perspective of Best coapproximation. https://arxiv.org/abs/2508.04971

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