On a singular part of an unbounded operator
type: Item
instance of: scholarly article
title: On a singular part of an unbounded operator
zbMATH Open document ID: 0657.47001
DOI: 10.4171/ZAA/279
author: S. H. Smith
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1988-01-01T00:00:00Z
review text: A densely defined linear operator A on a Hilbert space is said to be singular if, for each \(x\in R(A)\), there is a sequence \(y_ n\) in the domain of A such that \(y_ n\to 0\) and \(Ay_ n\to x\). The author gives a number of characterizations of singularity and related results. In particular, it is shown that if two operators are unitarily equivalent, then so are their canonical projections [in the sense of \textit{P. E. T. Jørgensen}, J. Funct. Anal. 39, 281-307 (1980; Zbl 0458.47034)].
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 47A65
zbMATH DE Number: 4073761
zbMATH Keywords: unbounded operator
zbMATH Keywords: singular operator
zbMATH Keywords: densely defined linear operator
zbMATH Keywords: Hilbert space
zbMATH Keywords: characterizations of singularity
reviewed by: Charles W. Groetsch
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/zaa/279
OpenAlex ID: W2567330310
description: scientific article; zbMATH DE number 4073761