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Construction of unbounded measures on the projectors of a Hilbert space
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“…For unbounded measures this is not a case, in general. More precisely, any positive singular bilinear form t generates by (3.1) a regular measure that is not completely-additive, see [Dvu3,Thm 3.7.6], [Lug2]. A criterion when a bilinear form t generates a completely additive measure on L(H), see [Lug2], [Dvu3,Thm 3.7.5]: A positive bilinear form t defines through (3.1) a σ-finite completely additive measure on L(H) iff for any M ∈ L(H),…”
Section: Gleason Measures On L(h) and Generalized Effect Algebrasmentioning
confidence: 99%
“…For unbounded measures this is not a case, in general. More precisely, any positive singular bilinear form t generates by (3.1) a regular measure that is not completely-additive, see [Dvu3,Thm 3.7.6], [Lug2]. A criterion when a bilinear form t generates a completely additive measure on L(H), see [Lug2], [Dvu3,Thm 3.7.5]: A positive bilinear form t defines through (3.1) a σ-finite completely additive measure on L(H) iff for any M ∈ L(H),…”
Section: Gleason Measures On L(h) and Generalized Effect Algebrasmentioning
confidence: 99%
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