On the nonintegrability property of the Fredholm resolvent of some integral operators
type: Item
instance of: scholarly article
title: On the nonintegrability property of the Fredholm resolvent of some integral operators
zbMATH Open document ID: 0917.47044
DOI: 10.1007/BF02673059
author: V. B. Korotkov
published in: Siberian Mathematical Journal
publication date: 1999-05-10T00:00:00Z
review text: Let \(L_2=L_2(X,\mu)\) be a separable space, with \(\mu\) a \(\sigma\)-finite measure that is not purely atomic. The author gives an example of an integral operator \(S\) in \(L_2\) such that \(S^3=0\) but, for every element \(\lambda\) of the resolvent set, neither the Fredholm resolvent \(F_{\lambda}=-\lambda S(S-\lambda I)^{-1}\) nor the operators \(S^2\) and \(F_{\lambda}^2\) are integral or partially integral operators.
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 45P05
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 1285467
zbMATH Keywords: Akhiezer operator
zbMATH Keywords: integral operator
zbMATH Keywords: Fredholm resolvent
zbMATH Keywords: partially integral operators
MaRDI profile type: Publication
cites work: On resolvents of intergral and partially integral operators
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description: scientific article; zbMATH DE number 1285467