Operators Reversing Orthogonality and Characterization of Inner Product Spaces

Document Type : Original Article

Author

Paweł Wójcik

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

10.22034/kjm.2017.44746

Abstract

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.

Keywords

Birkhoff orthogonality

orthogonality reversing mappings

characterizations of inner product spaces

Subjects

• 15 Linear and multilinear algebra; matrix theory
• 46 Functional analysis
• 47 Operator theory

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