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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 17, Fasc. 2,
pages 365 - 375
 

DILATION THEOREMS FOR POSITIVE OPERATOR-VALUED MEASURES

E. Hensz-Chądzyńska
R. Jajte
A. Paszkiewicz

Abstract: Let Q(D) be a positive operator-valued measure defined on a measurable space (X,S). This means that Q(D) : L (M, M, m)-- > L (M,M, m) 1 1 with Q(D)f > 0 for f > 0. Then Q(.) has a “dilation” of the form Q~(D) = 4EA1 EB1 e(D) _O_0 in (_O_, F,P). Namely, for some “identification” map i : _O_ --> M, the equality ~ (Q(D)f )o i = Q(D)(f o i) holds. The indicator operators 1e(D) are taken for a set e(D) with some s -lattice homomorphism e : S-- > F. Other dilation formulas of that type are collected.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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