On unbounded subnormal operators
type: Item
instance of: scholarly article
title: On unbounded subnormal operators
zbMATH Open document ID: 0677.47004
DOI: 10.1007/BF02874649
author: Arvind B. Patel
author: S. J. Bhatt
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1989-01-01T00:00:00Z
review text: An operator S with a dense domain D(S) in a Hilbert space H is called subnormal if there exists a normal operator N with a dense domain D(N) in a Hilbert space K such that \(H\subset K\), D(S)\(\subseteq D(N)\) and \(Nx=Sx\) for all \(x\in D(S)\). It is shown that some well-known theorems of bounded case remain valid for unbounded subnormal operators. Here are some instances. (i) Every subnormal operator admits a minimal normal extension. (ii) If \(\{N^{*j}N^ ix:\) \(x\in \cap^{\infty}_{1}D(S^ n)\), \(i,j=1,2,...\}\) is dense in K, then N is a minimal normal extension. (iii) If N is a minimal normal extension of S, then \(\sigma\) (N)\(\subseteq \sigma (S).\) The paper also contains some results which are particular to the unbounded case.
Mathematics Subject Classification ID: 47A20
Mathematics Subject Classification ID: 47B20
zbMATH DE Number: 4109405
zbMATH Keywords: normal operator
zbMATH Keywords: unbounded subnormal operators
zbMATH Keywords: minimal normal extension
MaRDI profile type: Publication
cites work: The space 𝐿^{𝜔} and convex topological rings
cites work: Formally Normal Operators Having no Normal Extensions
cites work: Q3930259
cites work: Q5602426
cites work: Q5521075
cites work: On the Spectra of Unbounded Subnormal Operators
cites work: Q3322696
cites work: Q3036123
cites work: Shorter Notes: A Formally Normal Operator having no Normal Extension
cites work: Q3333590
cites work: Q4720264
cites work: Q3475865
cites work: Q3873024
Recommended article: Q5286716
Recommended article: Unbounded subnormal operators and their models
Recommended article: On the Spectra of Unbounded Subnormal Operators
Recommended article: Q3984049
Recommended article: On subnormal operators
Recommended article: On unbounded hyponormal operators
Recommended article: ON A FRIEDRICHS EXTENSION RELATED TO UNBOUNDED SUBNORMAL OPERATORS
Recommended article: Unbounded operators having self‐adjoint, subnormal, or hyponormal powers
Recommended article: Q4224471
Recommended article: Unbounded subnormal composition operators in \(L^2\)-spaces
description: scientific article; zbMATH DE number 4109405