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Autumn 2016 Operators reversing orthogonality in normed spaces
Jacek Chmieliński
Adv. Oper. Theory 1(1): 8-14 (Autumn 2016). DOI: 10.22034/aot.1610.1021

Abstract

We consider linear operators $T: X \to X$ on a normed space $X$ which reverse orthogonality, i.e., satisfy the condition $$x \bot y \quad \Longrightarrow \quad Ty \bot Tx, \qquad x,y \in X,$$ where $\bot$ stands for Birkhoff orthogonality.

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Jacek Chmieliński. "Operators reversing orthogonality in normed spaces." Adv. Oper. Theory 1 (1) 8 - 14, Autumn 2016. https://doi.org/10.22034/aot.1610.1021

Information

Received: 2 October 2016; Accepted: 24 October 2016; Published: Autumn 2016
First available in Project Euclid: 4 December 2017

zbMATH: 06664781
MathSciNet: MR3721325
Digital Object Identifier: 10.22034/aot.1610.1021

Subjects:
Primary: 15A86
Secondary: 15A04 , 46B04 , 46B20 , 46C15 , 47A62 , 52A21

Keywords: Birkhoff orthogonality , characterizations of inner product spaces , linear similarities , orthogonality preserving mappings , orthogonality reversing mappings

Rights: Copyright © 2016 Tusi Mathematical Research Group

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Vol.1 • No. 1 • Autumn 2016
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