Geodesic
Orthogonally additive mappings on Hilbert modules
Dijana Ilišević1 ; Aleksej Turnšek2 ; Dilian Yang3
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
Studia Mathematica, Tome 221 (2014) no. 3, pp. 209-229

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm221-3-2
Keywords: study representation orthogonally additive mappings acting hilbert * modules hilbert * modules main results shows every continuous orthogonally additive mapping hilbert module mathcal mathcal mathcal mathcal mathcal complex normed space form varphi langle rangle where continuous additive mapping varphi continuous linear mapping

Dijana Ilišević 1 ; Aleksej Turnšek 2 ; Dilian Yang 3

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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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

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