On some subspaces of vector-valued continuous function space, from the perspective of Best coapproximation
Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Ghosh, Souvik, Paul, Kallol, Sain, Debmalya, Sohel, Shamim
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6910500830
Cites:
Cited by:
Related to: