Some remarks on Gleason measures
Volume 179 / 2007
Studia Mathematica 179 (2007), 99-115
MSC: 47B15, 28C05.
DOI: 10.4064/sm179-2-1
Abstract
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.
