Operators Reversing Orthogonality and Characterization of Inner Product Spaces

Document Type : Original Article


Institute of Mathematics, Pedagogical University of Cracow, Podchorążych 2, 30-084 Kraków, Poland.


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


Main Subjects