On a class of operators with finite rank self-commutators
type: Item
instance of: scholarly article
title: On a class of operators with finite rank self-commutators
zbMATH Open document ID: 0932.47019
DOI: 10.1007/BF01291839
published in: Integral Equations and Operator Theory
publication date: 2000-03-19T00:00:00Z
review text: This paper studies the class of pure operators \(A\) on a Hilbert space \(H\) satisfying \(\dim K_A< \infty\), where \(K_A= \bigvee^\infty_{n= 0} A^{*n}[A^*, A]H\). The main tool is a pair of matrices \(C_A= [A^*, A]|K_A\), and \(\Lambda_A= (A^*|K_A)^*\). A reproducing kernel Hilbert space model is introduced for a subclass of this class of operators. Some theorems are established for some subnormal operators as well as hyponormal operators in this class.
Mathematics Subject Classification ID: 47B20
Mathematics Subject Classification ID: 46E22
Mathematics Subject Classification ID: 47B32
zbMATH DE Number: 1310387
zbMATH Keywords: pure operators
zbMATH Keywords: reproducing kernel Hilbert space model
zbMATH Keywords: subnormal operators
zbMATH Keywords: hyponormal operators
author: Daoxing Xiao
reviewed by: Mahmoud Kutkut
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1310387