Extension of locally defined indefinite functions on ordered groups
type: Item
instance of: scholarly article
title: Extension of locally defined indefinite functions on ordered groups
zbMATH Open document ID: 1073.47023
author: R. Bruzual
author: M. Domínguez
published in: Integral Equations and Operator Theory
publication date: 2004-11-05T00:00:00Z
review text: The authors aim to unify several previously known results concerning the extensions of some operator-valued functions. Their framework involves operators on Krein spaces \(({\mathcal K},\langle .,. \rangle)\) and domains in ordered abelian archimedean groups \((\Omega, +)\). The extension problem for a function \(f:[-2a,2a]\to L({\mathcal K})\) consists in the existence of a function \(F:\Omega\to L({\mathcal K})\) such that \(F|_{[-2a,2a]}=f\). The authors' key notion is that of \(k\)-indefinite function of archimedean type. A remarkable result (Theorem 7.5) shows that if \(\Gamma\) is a semi-archimedean group with the indefinite extension property, then \(\Gamma\times\mathbb{Z}^d\), endowed with the lexicographic order and the product topology, has the indefinite extension property. Consequently, \(\mathbb{Z}^n\) and \(\mathbb{R}\times\mathbb{Z}^n\) have the indefinite extension property.
Mathematics Subject Classification ID: 47A56
Mathematics Subject Classification ID: 47B50
Mathematics Subject Classification ID: 46C20
Mathematics Subject Classification ID: 47D03
zbMATH DE Number: 2113886
zbMATH Keywords: operators in Krein spaces
zbMATH Keywords: operator valued functions
zbMATH Keywords: \(k\)-indefinite functions
zbMATH Keywords: Archimedian groups
zbMATH Keywords: indefinite extension property
reviewed by: Trandafir Balan
MaRDI profile type: Publication
full work available at URL: s00020-003-1223-2
OpenAlex ID: W1978223389
DOI: 10.1007/S00020-003-1223-2
description: scientific article; zbMATH DE number 2113886