This work is devoted to generalizing the Lebesgue decomposition and the Radon-Nikodym theorem to Gleason measures. For that purpose we introduce a notion of integral for operators with respect to a Gleason measure. Finally, we give an example showing that the Gleason theorem does not hold in non-separable Hilbert spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-2-1,
author = {P. De N\'apoli and M. C. Mariani},
title = {Some remarks on Gleason measures},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {99-115},
zbl = {1129.47021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-2-1}
}
P. De Nápoli; M. C. Mariani. Some remarks on Gleason measures. Studia Mathematica, Tome 178 (2007) pp. 99-115. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-2-1/