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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm221-3-2, author = {Dijana Ili\v sevi\'c and Aleksej Turn\v sek and Dilian Yang}, title = {Orthogonally additive mappings on Hilbert modules}, journal = {Studia Mathematica}, volume = {223}, year = {2014}, pages = {209-229}, zbl = {1304.46052}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm221-3-2} }
Dijana Ilišević; Aleksej Turnšek; Dilian Yang. Orthogonally additive mappings on Hilbert modules. Studia Mathematica, Tome 223 (2014) pp. 209-229. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm221-3-2/