We show that the result of Kato on the existence of a semigroup solving the Kolmogorov system of equations in l₁ can be generalized to a larger class of the so-called Kantorovich-Banach spaces. We also present a number of related generation results that can be proved using positivity methods, as well as some examples.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-3-2,
author = {Jacek Banasiak and Miros\l aw Lachowicz},
title = {Around the Kato generation theorem for semigroups},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {217-238},
zbl = {1115.47037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-3-2}
}
Jacek Banasiak; Mirosław Lachowicz. Around the Kato generation theorem for semigroups. Studia Mathematica, Tome 178 (2007) pp. 217-238. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-3-2/