We prove that differences of order-continuous operators acting between function spaces can be represented with a pseudo-kernel, proved the underlying measure spaces satisfy certain (rather weak) conditions. To see that part of these conditions are necessary, we show that the strict localizability of a measure space can be characterized by the existence of a pseudo-kernel for a certain operator.
@article{urn:eudml:doc:42569,
title = {Representation of operators by kernels.},
journal = {Collectanea Mathematica},
volume = {42},
year = {1991},
pages = {285-292},
zbl = {0779.47032},
mrnumber = {MR1203186},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:42569}
}
Stollmann, Peter. Representation of operators by kernels.. Collectanea Mathematica, Tome 42 (1991) pp. 285-292. http://gdmltest.u-ga.fr/item/urn:eudml:doc:42569/