On some algebraic properties of integral operators
type: Item
instance of: scholarly article
title: On some algebraic properties of integral operators
zbMATH Open document ID: 0877.45006
DOI: 10.1007/BF02106742
author: V. B. Korotkov
published in: Siberian Mathematical Journal
publication date: 1997-12-10T00:00:00Z
review text: The author proves two theorems about continuous linear operators. Is \(ABT\) an integral operator for every compact regular integral operator \(A\) in \(L_2\) and every compact Carleman integral operator \(B\) in \(L_2\) then \(T\) is a Hilbert-Schmidt integral operator. The second theorem is analogous, if \(KLTM\) only for compact regular integral operators \(K\) and \(M\) in \(L_2\). Two corollaries for each theorem contain statements about ideals of the set of all integral operators \(L\) and the ideal comprising Hilbert-Schmidt integral operators.
Mathematics Subject Classification ID: 45P05
Mathematics Subject Classification ID: 47B07
Mathematics Subject Classification ID: 47L20
zbMATH DE Number: 1023891
zbMATH Keywords: ideals of operators
zbMATH Keywords: compact Carleman integral operator
zbMATH Keywords: Hilbert-Schmidt integral operator
zbMATH Keywords: compact regular integral operators
reviewed by: Ulrich Kosel
MaRDI profile type: Publication
cites work: Ideals of sets of integral and partially integral operators
cites work: Q3041809
cites work: Q3996780
description: scientific article; zbMATH DE number 1023891