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On symmetricity of orthogonality with respect to numerical radius norm

  • Shamim Sohel
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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 𝒦(X) of compact operators on X.

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Cite

BibTeXRIS
BibTeX
@misc{sohel2026symmetricity,
  title = {{On symmetricity of orthogonality with respect to numerical radius norm}},
  author = {Shamim Sohel},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.27608},
  eprint = {2608.27608},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.27608},
}
RIS
TY  - UNPB
TI  - On symmetricity of orthogonality with respect to numerical radius norm
AU  - Shamim Sohel
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2608.27608
UR  - https://arxiv.org/abs/2608.27608
AB  - 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 𝒦(X) of compact operators on X.
ER  -