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

TL;DR

This paper investigates Birkhoff-James orthogonality and its local symmetry in various sequence spaces, characterizing isometries and extending the Banach-Lamperti theorem to these spaces.

Contribution

It provides new characterizations of local symmetry of Birkhoff-James orthogonality and extends the Banach-Lamperti theorem to several classical sequence spaces.

Findings

Characterization of local symmetry in sequence spaces

Isometry characterizations for these spaces

Extension of Banach-Lamperti theorem

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.