Local symmetry and smoothness in the space of vector-valued continuous functions

Mohit; Ranjana Jain

Local symmetry and smoothness in the space of vector-valued continuous functions

Functional Analysis 2025-04-07 v1

Authors: Mohit , Ranjana Jain

Abstract

In this article, we characterize the left symmetric points in $C(K,X)$ , where $K$ is a compact Hausdorff space and $X$ is a Banach space. We also provide necessary and sufficient conditions for the right symmetric points in $C(K,X)$ . Further, we identify the smooth points in the space $C_0(K,X)$ , $K$ being locally compact Hausdorff space and $X$ being a Banach space.

Keywords

symmetric points Banach space continuous functions smooth points compact Hausdorff space

Cite

@article{arxiv.2504.03371,
  title  = {Local symmetry and smoothness in the space of vector-valued continuous functions},
  author = {Mohit and Ranjana Jain},
  journal= {arXiv preprint arXiv:2504.03371},
  year   = {2025}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2411.03798

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