- Tytuł:
- Decomposition and disintegration of positive definite kernels on convex *-semigroups
- Autorzy:
- Stochel, Jan
- Powiązania:
- https://bibliotekanauki.pl/articles/1312141.pdf
- Data publikacji:
- 1992
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- 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 a positive definite holomorphic mapping on the open unit ball $_•$ of a commutative Banach *-algebra is supported by the holomorphic characters of $_•$. A relationship between positive definiteness and complete positivity is established in the case of commutative W*-algebras.
- Źródło:
-
Annales Polonici Mathematici; 1991-1992, 56, 3; 243-294
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł