On the nonintegrability property of the Fredholm resolvent of some integral operators
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.
scientific article; zbMATH DE number 1285467