JEDNOSTKA NAUKOWA KATEGORII A+

Orthogonally additive mappings on Hilbert modules

Tom 221 / 2014

Dijana Ilišević, Aleksej Turnšek, Dilian Yang 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.

Autorzy

  • Dijana IliševićDepartment of Mathematics
    University of Zagreb
    Bijenička 30
    10000 Zagreb, Croatia
    e-mail
  • Aleksej TurnšekFaculty 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
    e-mail
  • Dilian YangDepartment of Mathematics & Statistics
    University of Windsor
    Windsor, ON N9B 3P4, Canada
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek