Domination of unbounded operators and commutativity.
type: Item
instance of: scholarly article
title: Domination of unbounded operators and commutativity.
zbMATH Open document ID: 1037.47003
author: Jan Stochel
author: Franciszek Hugon Szafraniec
published in: Journal of the Mathematical Society of Japan
publication date: 2003-06-30T00:00:00Z
review text: The authors prove that pointwise commuting formally normal operators which are dominated by a single essentially normal operator are essentially normal, and their closures commute spectrally. It is also shown that for a formally normal operator \(A\), the normality of a polynomial \(p(A)\) implies the essential normality of \(A\) and of all polynomials of \(A\) whose degrees do not exceed the degree of \(p\). For commuting families of formally normal operators, some Nelson type criteria of essential spectral commutation are obtained; these results are in fact new even for symmetric operators, where the condition upon the sum of their squares may now be substituted by conditions upon certain more general polynomials. In terms of domination, the authors also treat the problem of joint subnormality for systems of operators. Applications to multi-dimensional moment problems are discussed. In particular, determinacy conditions are found for the multi-dimensional Hamburger and complex moment problems.
reviewed by: Anatoly N. Kochubei
Mathematics Subject Classification ID: 47A13
Mathematics Subject Classification ID: 47B20
Mathematics Subject Classification ID: 47B15
Mathematics Subject Classification ID: 47A57
Mathematics Subject Classification ID: 47B25
zbMATH DE Number: 1943318
zbMATH Keywords: formally normal operator
zbMATH Keywords: essentially normal operator
zbMATH Keywords: multi-dimensional moment problem
zbMATH Keywords: spectral commutation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/1191419124
OpenAlex ID: W2070956180
DOI: 10.2969/JMSJ/1191419124
description: scientific article; zbMATH DE number 1943318