Symmetry of Birkhoff-James orthogonality of operators defined between infinite dimensional Banach spaces
arXiv:1807.11166 · doi:10.1016/j.laa.2018.10.022
Abstract
We study left symmetric bounded linear operators in the sense of Birkhoff-James orthogonality defined between infinite dimensional Banach spaces. We prove that a bounded linear operator defined between two strictly convex Banach spaces is left symmetric if and only if it is zero operator when the domain space is reflexive and Kadets-Klee. We exhibit a non-zero left symmetric operator when the spaces are not strictly convex. We also study right symmetric bounded linear operators between infinite dimensional Banach spaces.
10 pages