Paweł Wójcik
Abstract
In this short paper we answer a question posed by Chmielinski 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.
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In this short paper we answer a question posed by Chmielinski 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.
Key concepts: Inner product space, Orthogonality, Mathematics, Reversing, Product (mathematics), Dimension (graph theory), Characterization (materials science), Operator theory