New proof of Naimark's theorem on the existence of nonpositive invariant subspaces for commuting families of unitary operators in Pontryagin spaces
type: Item
instance of: scholarly article
title: New proof of Naimark's theorem on the existence of nonpositive invariant subspaces for commuting families of unitary operators in Pontryagin spaces
zbMATH Open document ID: 0713.47035
DOI: 10.1007/BF01302935
published in: Monatshefte für Mathematik
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178466
review text: In the paper we give a new and short proof of \textit{M. A. Naimark}'s theorem [Acta Sci. Math. 24, 177-189 (1963; Zbl 0115.333)] asserting that for every commuting family \({\mathcal F}\) of unitary operators in a \(\pi_ k\)-space \(\Pi_ k\) there exists a k-dimensional, nonpositive subspace invariant under \({\mathcal F}\).
Mathematics Subject Classification ID: 47B50
Mathematics Subject Classification ID: 47A15
zbMATH DE Number: 4173726
zbMATH Keywords: Naimark's theorem on the existence of nonpositive invariant subspaces for commuting families of unitary operators in Pontryagin spaces
author: Zoltán Sasvári
MaRDI profile type: Publication
cites work: Sequences with finitely many negative squares
cites work: Q4743338
cites work: Q5724178
OpenAlex ID: W374529905
description: scientific article; zbMATH DE number 4173726