Operators Reversing Orthogonality and Characterization of Inner Product Spaces

Abstract

In this short paper we answer a question posed by Chmieliński in [Adv. Oper. Theory, 1 (2016), no. 1, 8-14].<br /> Namely, we prove that among normed spaces of dimension greater than two,<br />only inner product spaces admit nonzero linear operators which reverse the Birkhoff orthogonality.