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

Abstract

We study Birkhoff-James orthogonality and its local symmetry in some sequence spaces namely ${\ell }_p,$ for $1\le p\le \infty$, $p\ne 2$, $c$, $c_0$ 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.