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

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.