Some remarks on Gleason measures

• Autorzy: P. De Nápoli , M. C. Mariani
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 28C05: Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
• 47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 179
• Numer: 2
• Strony: 99-115

Daty

wydano

2007

Twórcy

autor

P. De Nápoli

• Departamento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires, Argentina

autor

M. C. Mariani

• Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003-0001, U.S.A.

Identyfikatory

DOI

10.4064/sm179-2-1