WitrynaAn extension of the Naimark dilation theorem to free semigroups is considered. This is used to construct a large class of positive definite operator-valued kernels on the unital free semigroup on n generators and to study the class Cρ (ρ>0) of ρ-contractive sequences of operators. The dilation theorems are also used to extend the … WitrynaDilation theorem for contractions Sz.-Nagy's dilation theorem , proved in 1953, states that for any contraction T on a Hilbert space H , there is a unitary operator U on a larger Hilbert space K ⊇ H such that if P is the orthogonal projection of K onto H then T n = P U n P for all n > 0.

Vol. 79 (2024) REPORTS ON MATHEMATICAL PHYSICS No. 2

Witryna[15] W. Mlak, Unitary dilations of contraction operators, Rozprawy Mat., Warszawa 1965. [16] W. Mlak, A note on general dilation theorems (to appear in Banach … Witryna28 maj 2010 · The key tools in the proof of the main result are: 1) theorem 4.5 where we prove that two POVMs are jointly measurable if and only if they can be dilated (Naimark's dilation) to two jointly ... easy cream cheese danish with puff pastry

(PDF) Notes on Naimark

Witrynaof Naimark dilations, show that there is a minimal element and that it is unique. Minimality is a consequence of the partial ordered structure and coincides with the … Witryna16 lis 2024 · Naimark's dilation theorem in papers and textbooks is usually stated as: Let E be a regular, positive, B ( H) -valued measure on X. Then there exists a Hilbert … easy cream cheese banana bread