Open Access
2015 Linear mappings approximately preserving orthogonality in real normed spaces
Paweł Wójcik
Banach J. Math. Anal. 9(2): 134-141 (2015). DOI: 10.15352/bjma/09-2-11


In a normed space we introduce an exact and approximate orthogonality relation. We consider classes of linear mappings approximately preserving this kind of orthogonality. We show that, in particular, the property that a linear mapping approximately preserves the $B$-orthogonality is equivalent to that it approximately preserves the $\rho,\rho_+$-orthogonality (although these orthogonalities need not be equivalent). Moreover, we show that every approximately orthogonality preserving linear mapping is necessarily a scalar multiple of an almost isometry.


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Paweł Wójcik . "Linear mappings approximately preserving orthogonality in real normed spaces." Banach J. Math. Anal. 9 (2) 134 - 141, 2015.


Published: 2015
First available in Project Euclid: 19 December 2014

zbMATH: 1334.46015
MathSciNet: MR3296111
Digital Object Identifier: 10.15352/bjma/09-2-11

Primary: 46B20
Secondary: 46C50 , 47B99

Keywords: approximate orthogonality , linear mappings orthogonality preserving , norm derivative , Orthogonality in normed spaces

Rights: Copyright © 2015 Tusi Mathematical Research Group

Vol.9 • No. 2 • 2015
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