Orthogonality and additivity modulo a subgroup
type: Item
instance of: scholarly article
title: Orthogonality and additivity modulo a subgroup
zbMATH Open document ID: 0789.39004
DOI: 10.1007/BF01833994
author: Karol Baron
author: Jürg Rätz
published in: Aequationes Mathematicae
publication date: 1994-02-06T00:00:00Z
full work available at URL: https://eudml.org/doc/137536
review text: Let \(E\) be a real inner product space of dimension at least 2, \(F\) a topological Abelian group, and \(K\) a discrete subgroup of \(F\). The main result is given in the following theorem: Suppose \(F\) is continuously divisible by 2. If \(f: E\to F\) fulfils the condition \(f(x+y)-f(x)-f(y)\in K\) for all orthogonal \(x,y\in E\) and it is continuous at the origin, then there exist continuous additive functions \(a: \mathbb{R}\to F\) and \(A: E\to F\) such that \(f(x)-a(\| x\|^ 2)- A(x)\in K\) for every \(x\in E\).
reviewed by: Ilie Corovei
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 493230
zbMATH Keywords: orthogonality
zbMATH Keywords: additivity modulo a subgroup
zbMATH Keywords: inner product space
zbMATH Keywords: topological Abelian group
zbMATH Keywords: continuous additive functions
MaRDI profile type: Publication
cites work: On the Pexider difference
cites work: Q4084684
cites work: On orthogonally additive mappings
OpenAlex ID: W2088316951
description: scientific article; zbMATH DE number 493230