Orthogonally additive mappings on Hilbert modules

• Autorzy: Dijana Ilišević , Aleksej Turnšek , Dilian Yang
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47B48: Operators on Banach algebras
• 39B55: Orthogonal additivity and other conditional equations
• 46L08: C * -modules

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 221
• Numer: 3
• Strony: 209-229

Daty

wydano

2014

Twórcy

autor

Dijana Ilišević

• Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia

autor

Aleksej Turnšek

• Faculty of Maritime Studies and Transport, University of Ljubljana, Pot pomorščakov 4, 6320 Portorož, Slovenia
• Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia

autor

Dilian Yang

• Department of Mathematics & Statistics, University of Windsor, Windsor, ON N9B 3P4, Canada

Identyfikatory

DOI

10.4064/sm221-3-2