It is shown that reducing bands of measures yield decompositions not only of an operator representation itself, but also of its commutant. This has many consequences for commuting Hilbert space representations and for commuting operators on Hilbert spaces. Among other things, it enables one to construct a Lebesgue-type decomposition of several commuting contractions without assuming any von Neumann-type inequality.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm151-1-6,
author = {Marek Kosiek},
title = {Fuglede-type decompositions of representations},
journal = {Studia Mathematica},
volume = {151},
year = {2002},
pages = {87-98},
zbl = {1005.47018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm151-1-6}
}
Marek Kosiek. Fuglede-type decompositions of representations. Studia Mathematica, Tome 151 (2002) pp. 87-98. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm151-1-6/