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On the Stability of Orthogonal Additivity

Włodzimierz Fechner, Justyna Sikorska (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

We deal with the stability of the orthogonal additivity equation, presenting a new approach to the proof of a 1995 result of R, Ger and the second author. We sharpen the estimate obtained there. Moreover, we work in more general settings, providing an axiomatic framework which covers much more cases than considered before by other authors.

Orthogonally additive mappings on Hilbert modules

Dijana Ilišević, Aleksej Turnšek, Dilian Yang (2014)

Studia Mathematica

We study the representation of orthogonally additive mappings acting on Hilbert C*-modules and Hilbert H*-modules. One of our main results shows that every continuous orthogonally additive mapping f from a Hilbert module W over 𝓚(𝓗) or 𝓗𝓢(𝓗) to a complex normed space is of the form f(x) = T(x) + Φ(⟨x,x⟩) for all x ∈ W, where T is a continuous additive mapping, and Φ is a continuous linear mapping.

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