On left ideals of sets of partially integral operators
type: Item
instance of: scholarly article
title: On left ideals of sets of partially integral operators
zbMATH Open document ID: 0888.47030
DOI: 10.1007/BF02104819
author: V. B. Korotkov
published in: Siberian Mathematical Journal
publication date: 1998-05-13T00:00:00Z
review text: The operators of the title take the form \(Tf(s)=\int_X K(s,t)f(t) d\mu(t)\) where \((X,\mu)\) is a finite measure space which is not purely atomic and \(K\) is a complex--valued measurable kernel defined on \(X\times X\). The author presents two sufficient conditions for such an operator to map \(L^2(X,\mu)\) into an ellipsoid, i.e., for the existence of a square summable sequence \(\{z_n\}\) in \(L^2\) such that for each \(f\in L^2\), it is possible to express \(Tf=\sum\alpha_nz_n\) with square summable (scalar) coefficients.
Mathematics Subject Classification ID: 47G10
zbMATH DE Number: 917071
zbMATH Keywords: ellipsoid
zbMATH Keywords: compact operator
zbMATH Keywords: partially integral operators
reviewed by: Edward A. Azoff
MaRDI profile type: Publication
cites work: Q3041809
cites work: Q4197100
cites work: Ideals of sets of integral and partially integral operators
full work available at URL: https://doi.org/10.1007/bf02104819
OpenAlex ID: W2062361266
description: scientific article; zbMATH DE number 917071