On the stability of the orthogonality equation and the orthogonality-preserving property with two unknown functions

DOI10.1215/17358787-3649656zbMath1352.39019OpenAlexW2524237842MaRDI QIDQ728000

Radosław ~Łukasik, Paweł Wójcik, Jacek Chmieliński

Publication date: 21 December 2016

Published in: Banach Journal of Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.bjma/1475267150

zbMATH Keywords

Hilbert spaceslinear isometriesorthogonality equationorthogonality-preserving mappings

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Stability, separation, extension, and related topics for functional equations (39B82) Equations involving linear operators, with operator unknowns (47A62) Functional equations for functions with more general domains and/or ranges (39B52) Linear preserver problems (15A86)

Related Items (14)

Orthogonality preserving property for pairs of operators on Hilbert \(C^*\)-modules ⋮ Orthogonality Hilbert 𝒜-modules and operators preserving multi-𝒜-linearity ⋮ The operator-valued parallelism and norm-parallelism in matrices ⋮ Decomposition of two functions in the orthogonality equation ⋮ A note on the orthogonality equation with two functions ⋮ Characterizations of norm-parallelism in spaces of continuous functions ⋮ Unnamed Item ⋮ Birkhoff–James Orthogonality Reversing Property and Its Stability ⋮ On Exact and Approximate Orthogonalities Based on Norm Derivatives ⋮ APPROXIMATELY ANGLE PRESERVING MAPPINGS ⋮ Orthogonally \(a\)-Jensen mappings on \(C^*\)-modules ⋮ Approximately orthogonality preserving maps in Krein spaces ⋮ Parallelism in Hilbert \(K(\mathcal{H})\)-modules ⋮ Characterization of real inner product spaces by Hermite-Hadamard type orthogonalities

Cites Work

• Unnamed Item
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• Orthogonality equation with two unknown functions
• Decomposition of two functions in the orthogonality equation
• AOP mappings and the distance to the scalar multiples of isometries
• Hyers-Ulam-Rassias stability of functional equations in nonlinear analysis
• Mappings approximately preserving orthogonality in normed spaces
• Linear mappings approximately preserving orthogonality
• Orthogonalities and functional equations
• Approximate Roberts orthogonality
• Decomposition of mappings approximately inner product preserving
• Stability of the orthogonality preserving property in finite-dimensional inner product spaces
• Linear maps preserving orthogonality
• On mappings approximately preserving orthogonality
• A generalized numerical range: the range of a constrained sesquilinear form
• Approximately bisectrix-orthogonality preserving mappings
• On the Stability of the Linear Functional Equation
• Stability of functional equations in several variables

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