A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Kolmogorov Decompositions and Extremality Conditions for Positive Covariant Kernels
Tekijät: Erkka Haapasalo, Juha-Pekka Pellonpää
Kustantaja: PERGAMON-ELSEVIER SCIENCE LTD
Julkaisuvuosi: 2019
Journal: Reports on Mathematical Physics
Tietokannassa oleva lehden nimi: REPORTS ON MATHEMATICAL PHYSICS
Lehden akronyymi: REP MATH PHYS
Vuosikerta: 83
Numero: 2
Aloitussivu: 253
Lopetussivu: 271
Sivujen määrä: 19
ISSN: 0034-4877
DOI: https://doi.org/10.1016/S0034-4877(19)30042-4
Tiivistelmä
We study positive kernels on X x X, where X is a set equipped with an action of a group, and taking values in the set of A-sesquilinear forms on a (not necessarily Hilbert) module over a C*-algebra A. These maps are assumed to be covariant with respect to the group action on X and a representation of the group in the set of invertible (A-linear) module maps. Such maps are generalizations of covariant instruments appearing in quantum theory of measurement. Minimal Kolmogorov decompositions for positive covariant kernels are given in this paper. We find necessary and sufficient conditions for extreme elements in certain convex subsets of positive covariant kernels and also study extreme rays of these sets.
We study positive kernels on X x X, where X is a set equipped with an action of a group, and taking values in the set of A-sesquilinear forms on a (not necessarily Hilbert) module over a C*-algebra A. These maps are assumed to be covariant with respect to the group action on X and a representation of the group in the set of invertible (A-linear) module maps. Such maps are generalizations of covariant instruments appearing in quantum theory of measurement. Minimal Kolmogorov decompositions for positive covariant kernels are given in this paper. We find necessary and sufficient conditions for extreme elements in certain convex subsets of positive covariant kernels and also study extreme rays of these sets.
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