Orthogonally additive mappings on Hilbert modules
Tom 221 / 2014
Studia Mathematica 221 (2014), 209-229
MSC: Primary 46L08; Secondary 39B55, 47B48.
DOI: 10.4064/sm221-3-2
Streszczenie
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.
