Orthogonally Additive Mappings on Hilbert Modules

2013/04/26 by Ilisevic, Dijana, Turnsek, Aleksej, Yang, Dilian
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1304.7207

Abstract

In this paper, 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 \H§(\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.

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