The index of a pair of projections
type: Item
instance of: scholarly article
title: The index of a pair of projections
zbMATH Open document ID: 0822.47033
author: J. E. Avron
author: B. Simon
author: Ruedi Seiler
published in: Journal of Functional Analysis
publication date: 1995-10-22T00:00:00Z
review text: The authors discuss pairs of self-adjoint projections with \(P- Q\in {\mathcal T}_{2n+ 1}\), the trace ideal, and prove that for \(m\geq n\), \[ \text{tr}(P- Q)^{2m+ 1}= \text{tr}(P- Q)^{2n+ 1}= \dim(\text{Ker } Q\cap \text{Ran } P)- \dim(\text{Ker } P\cap \text{Ran } Q) \] is an integer. They also prove that there exists a unitary \(V\) interchanging \(P\) and \(Q\) if and only if this integer is 0.
Mathematics Subject Classification ID: 47B47
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 47B15
zbMATH DE Number: 599757
zbMATH Keywords: self-adjoint projections
zbMATH Keywords: trace ideal
MaRDI profile type: Publication
full work available at URL: jfan.1994.1031
OpenAlex ID: W1973176771
DOI: 10.1006/JFAN.1994.1031
description: scientific article; zbMATH DE number 599757