Mappings approximately preserving orthogonality in normed spaces

DOI10.1016/j.na.2010.08.007zbMath1208.46016OpenAlexW2061338761MaRDI QIDQ607099

Blaž Mojškerc, Aleksej Turnšek

Publication date: 19 November 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.08.007

zbMATH Keywords

stabilityisometryBirkhoff-James orthogonalityapproximate orthogonalityorthogonality preserving mapping

Mathematics Subject Classification ID

Stability, separation, extension, and related topics for functional equations (39B82) Geometry and structure of normed linear spaces (46B20) Special classes of linear operators (47B99)

Related Items (20)

Mappings approximately preserving angles ⋮ A Birkhoff-James cosine function for normed linear spaces ⋮ Approximate Birkhoff-James Orthogonality in Normed Linear Spaces and Related Topics ⋮ Approximate orthogonality in normed spaces and its applications ⋮ Linear mappings approximately preserving \(\rho_\ast\)-orthogonality ⋮ Approximate Birkhoff orthogonalities in normed spaces ⋮ On mappings approximately transferring relations in finite-dimensional normed spaces ⋮ Birkhoff–James Orthogonality Reversing Property and Its Stability ⋮ On Exact and Approximate Orthogonalities Based on Norm Derivatives ⋮ Approximate symmetry of Birkhoff orthogonality ⋮ On certain basis connected with operator and its applications ⋮ On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces ⋮ AOP mappings and the distance to the scalar multiples of isometries ⋮ Multiplicative perturbation bounds for multivariate multiple linear regression in Schatten \(p\)-norms ⋮ An identity for \((\delta,\varepsilon)\)-approximately orthogonality preserving mappings ⋮ On the stability of the orthogonality equation and the orthogonality-preserving property with two unknown functions ⋮ Approximate \(\rho_\lambda^v\)-orthogonality and its preservation ⋮ Linear mappings approximately preserving orthogonality in real normed spaces ⋮ Orthogonalities and functional equations ⋮ Approximate Roberts orthogonality

Cites Work

• Banach spaces with trivial isometries
• Small into isomorphism on \(L_ p \)spaces
• On mappings approximately preserving orthogonality
• Isosceles-orthogonality preserving property and its stability
• On maps that preserve orthogonality in normed spaces
• Small Into-Isomorphisms Between Spaces of Continuous Functions
• Operators preserving orthogonality are isometries
• Orthogonality and Linear Functionals in Normed Linear Spaces
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