Orthogonally additive mappings on Hilbert modules

Dijana Ilišević, Aleksej Turnšek, and Dilian Yang. "Orthogonally additive mappings on Hilbert modules." Studia Mathematica 221.3 (2014): 209-229. <http://eudml.org/doc/285873>.

@article{DijanaIlišević2014,
abstract = {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.},
author = {Dijana Ilišević, Aleksej Turnšek, Dilian Yang},
journal = {Studia Mathematica},
keywords = {orthogonally additive mapping; Hilbert -module; Hilbert -module; orthogonality preserving mapping},
language = {eng},
number = {3},
pages = {209-229},
title = {Orthogonally additive mappings on Hilbert modules},
url = {http://eudml.org/doc/285873},
volume = {221},
year = {2014},
}

TY - JOUR
AU - Dijana Ilišević
AU - Aleksej Turnšek
AU - Dilian Yang
TI - Orthogonally additive mappings on Hilbert modules
JO - Studia Mathematica
PY - 2014
VL - 221
IS - 3
SP - 209
EP - 229
AB - 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.
LA - eng
KW - orthogonally additive mapping; Hilbert -module; Hilbert -module; orthogonality preserving mapping
UR - http://eudml.org/doc/285873
ER -