Birkhoff-James Orthogonality and Its Local Symmetry in Some Sequence Spaces

Babhrubahan Bose; Saikat Roy; Debmalya Sain

Birkhoff-James Orthogonality and Its Local Symmetry in Some Sequence Spaces

Functional Analysis 2022-05-25 v1

Authors: Babhrubahan Bose , Saikat Roy , Debmalya Sain

Abstract

We study Birkhoff-James orthogonality and its local symmetry in some sequence spaces namely $\ell_p,$ for $1\leq p\leq\infty$ , $p\neq2$ , $c$ , $c_0$ and $c_{00}$ . Using the characterization of the local symmetry of Birkhoff-James orthogonality, we characterize isometries of each of these spaces onto itself and obtain the Banach-Lamperti theorem for onto operators on the sequence spaces.

Keywords

Birkhoff-James orthogonality local symmetry sequence spaces isometries Banach-Lamperti theorem ell_p spaces

Cite

@article{arxiv.2205.11586,
  title  = {Birkhoff-James Orthogonality and Its Local Symmetry in Some Sequence Spaces},
  author = {Babhrubahan Bose and Saikat Roy and Debmalya Sain},
  journal= {arXiv preprint arXiv:2205.11586},
  year   = {2022}
}

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