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Chmieliński, Jacek; Wójcik, Paweł

On a \(\rho\)-orthogonality. (English) Zbl 1208.46015

Aequationes Math. 80, No. 1-2, 45-55 (2010).
Summary: In a normed space we introduce an exact and approximate orthogonality relation connected with “norm derivatives” \({\rho^{\prime}_{\pm}}\). We also consider classes of linear mappings preserving (exactly and approximately) this kind of orthogonality.

Cited in 2 Reviews
Cited in 28 Documents

MSC:

46B20 Geometry and structure of normed linear spaces
46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.)
39B82 Stability, separation, extension, and related topics for functional equations

Keywords:

orthogonality; approximate orthogonality; orthogonality preserving mappings; norm derivative
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References:

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