Near subnormal operators and subnormal operators
type: Item
instance of: scholarly article
title: Near subnormal operators and subnormal operators
zbMATH Open document ID: 0702.47012
DOI: 10.1007/BF02903841
author: Jipu Ma
author: Wang Gongbao
published in: Science in China. Series A
publication date: 1990-01-01T00:00:00Z
review text: A Hilbert space operator \(A\in B(H)\) is called a D-near subnormal operator if \(D\geq M^*ADA\) for some positive \(D\in B(H)\) and some positive constant M. In case \(D=A^*A-AA^*\geq 0\) and A is D-near subnormal, A is called a near subnormal operator. It is shown that every subnormal operator is near subnormal but the converse is false. Also, every hyponormal operator is trivially near subnormal but, again, the converse is false. The example of a nonsubnormal operator which is near subnormal is based on a criterion of subnormal operators which is the main result of the paper. The criterion involves sequences \(D_ n\) and \(B_ n\) of operators such that \[ D_ 0=A^*A-AA^*,\quad B_ 0=A,\quad B_ 1=D_ 0^{1/2} B_ 0D_ 0^{+1/2},\quad B_ n=D^{1/2}_{n-1} B_{n-1}D^{+1/2}_{n-1},\quad D_ n=Q_{B_ n}+D_{n-1}, \] where \(D^{+1/2}\) denotes the Moore-Penrose inverse of \(D^{1/2}\).
Mathematics Subject Classification ID: 47B20
Mathematics Subject Classification ID: 47A05
zbMATH DE Number: 4151159
zbMATH Keywords: near subnormal operator
zbMATH Keywords: hyponormal operator
zbMATH Keywords: example of a nonsubnormal operator which is near subnormal
zbMATH Keywords: Moore-Penrose inverse
MaRDI profile type: Publication
cites work: Sufficient and necessary conditions for Moore-Penrose inverses \(A_ x^ +\) to be continuous
cites work: (1. 2) inverses of operators between Banach spaces and local conjugacy theorem
cites work: Q4115244
cites work: Convergence of Newton-like methods for singular operator equations using outer inverses
cites work: Q3312749
cites work: Dimensions of subspaces of a Hilbert space and index of the semi-Fredholm operator
cites work: Generalized indices of operators in \(B(H)\)
full work available at URL: https://doi.org/10.1007/bf02903841
OpenAlex ID: W2995990019
description: scientific article; zbMATH DE number 4151159