Invariant subspace lattices that complement every subspace
type: Item
instance of: scholarly article
title: Invariant subspace lattices that complement every subspace
zbMATH Open document ID: 0621.47009
author: Domingo A. Herrero
author: Che-Kao Fong
author: Leiba Rodman
published in: Illinois Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: The following three statements are equivalent for an operator T acting on a complex Hilbert space H: (i) Given a subspace M of H, there exists R in Lat T (the lattice of all invariant subspaces of T) such that \(M\cap R=\{0\}\) and \(M+R=H\); that is, R complements M; (ii) Given a finite chain of subspaces \(M_ 1\subset M_ 2\subset...\subset M_ m\) in H, there exists a finite chain \(R_ 1\supset R_ 2\supset...\supset R_ m\) in Lat T such that \(R_ j\) complements \(M_ j\) for all \(j=1,2,...,m;\) (iii) T is similar to a normal operator with finite spectrum.
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 47L30
Mathematics Subject Classification ID: 47A65
zbMATH DE Number: 4007027
zbMATH Keywords: complemented subspace
zbMATH Keywords: lattice of all invariant subspaces
zbMATH Keywords: similar to a normal operator with finite spectrum
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4007027