On a characterization of linear operators
type: Item
instance of: scholarly article
title: On a characterization of linear operators
zbMATH Open document ID: 0867.47006
DOI: 10.1007/BF00114419
author: László Székelyhidi
published in: Acta Mathematica Hungarica
publication date: 1997-08-04T00:00:00Z
review text: Main result: Let \(X\) be a real or complex vector space and let \(B\) be a normed space. The function \(f:X\to B\) is linear if and only if the function \[ (x,y,\lambda)\mapsto f(\lambda x+y)-\lambda f(x)-f(y) \] remains bounded for large \(\lambda\). The author claims that this statement holds also if \(B\) is a locally convex topological vector space.
Mathematics Subject Classification ID: 47A05
zbMATH DE Number: 897185
zbMATH Keywords: linear operator bounded function
zbMATH Keywords: bounded function
zbMATH Keywords: locally convex topological vector space
reviewed by: Danuta Przeworska-Rolewicz
MaRDI profile type: Publication
cites work: On the Stability of the Linear Functional Equation
cites work: Approximate homomorphisms
cites work: The stability of multiplicative semigroup homomorphisms to real normed algebras.
cites work: An abstract superstability theorem
full work available at URL: https://doi.org/10.1007/bf00114419
OpenAlex ID: W1836115381
description: scientific article; zbMATH DE number 897185