Year: 2026
Type: preprint
Abstract: We study Birkhoff-James orthogonality and local symmetric points in the space $C(K,X)$ of vector-valued continuous functions equipped with a numerical-radius type (semi-)norm. We extend the theory of abstract numerical ranges to semi-normed spaces and obtain complete characterizations of the left and right symmetric points of $C(K,X)$ with respect to the numerical-radius (semi-) norm. We also establish corresponding results for the space $\mathcal{K}(X)$ of compact operators on $X$.
Source: arXiv (Cornell University)
Author: Sohel, Shamim
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204850310