Symmetry of Birkhoff James orthogonality of operators defined between infinite dimensional Banach spaces

摘要

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. (C) 2018 Elsevier Inc. All rights reserved.