1Department of Mathematics University of Zagreb Bijenička 30 10000 Zagreb, Croatia 2Faculty of Maritime Studies and Transport University of Ljubljana Pot pomorščakov 4 6320 Portorož, Slovenia and Institute of Mathematics, Physics and Mechanics Jadranska 19 1000 Ljubljana, Slovenia 3Department of Mathematics & Statistics University of Windsor Windsor, ON N9B 3P4, Canada
Studia Mathematica, Tome 221 (2014) no. 3, pp. 209-229
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 $\mathcal{K}(\mathcal{H})$ or $\mathcal{H}\mathcal{S}(\mathcal{H})$
to a complex normed space is of the form
$f(x)=T(x)+\varPhi(\langle x, x \rangle)$ for all $x\in W$,
where $T$ is a continuous additive mapping, and $\varPhi$ is a continuous linear mapping.
1
Department of Mathematics University of Zagreb Bijenička 30 10000 Zagreb, Croatia
2
Faculty of Maritime Studies and Transport University of Ljubljana Pot pomorščakov 4 6320 Portorož, Slovenia and Institute of Mathematics, Physics and Mechanics Jadranska 19 1000 Ljubljana, Slovenia
3
Department of Mathematics & Statistics University of Windsor Windsor, ON N9B 3P4, Canada
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title = {Orthogonally additive mappings on {Hilbert} modules},
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Dijana Ilišević; Aleksej Turnšek; Dilian Yang. Orthogonally additive mappings on Hilbert modules. Studia Mathematica, Tome 221 (2014) no. 3, pp. 209-229. doi: 10.4064/sm221-3-2
