Displaying similar documents to “Representing measures for the disc algebra and for the ball algebra”

Products and projective limits of function spaces

Miroslav Kačena (2008)

Commentationes Mathematicae Universitatis Carolinae

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We introduce a notion of a product and projective limit of function spaces. We show that the Choquet boundary of the product space is the product of Choquet boundaries. Next we show that the product of simplicial spaces is simplicial. We also show that the maximal measures on the product space are exactly those with maximal projections. We show similar characterizations of the Choquet boundary and the space of maximal measures for the projective limit of function spaces under some additional...

Decomposition and disintegration of positive definite kernels on convex *-semigroups

Jan Stochel (1992)

Annales Polonici Mathematici

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The paper deals with operator-valued positive definite kernels on a convex *-semigroup whose Kolmogorov-Aronszajn type factorizations induce *-semigroups of bounded shift operators. Any such kernel Φ has a canonical decomposition into a degenerate and a nondegenerate part. In case is commutative, Φ can be disintegrated with respect to some tight positive operator-valued measure defined on the characters of if and only if Φ is nondegenerate. It is proved that a representing measure of...