Displaying similar documents to “On the extension problem for unbounded measures on projections”

Some remarks on Gleason measures

P. De Nápoli, M. C. Mariani (2007)

Studia Mathematica

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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.

Fuglede-type decompositions of representations

Marek Kosiek (2002)

Studia Mathematica

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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.