Physics – Quantum Physics
Scientific paper
2006-09-08
Rep. Math. Phys. 58 (2006) 375-393
Physics
Quantum Physics
16 pages, no figures, to be published in Reports of Mathematical Physics; corrected typos
Scientific paper
10.1016/S0034-4877(06)80959-6
Measures with values in the set of sesquilinear forms on a subspace of a Hilbert space are of interest in quantum mechanics, since they can be interpreted as observables with only a restricted set of possible measurement preparations. In this paper, we consider the question under which conditions such a measure extends to an operator valued measure, in the concrete setting where the measure is defined on the Borel sets of the interval $[0,2\pi)$ and is covariant with respect to shifts. In this case, the measure is characterized with a single infinite matrix, and it turns out that a basic sufficient condition for the extensibility is that the matrix be a Schur multiplier. Accordingly, we also study the connection between the extensibility problem and the theory of Schur multipliers. In particular, we define some new norms for Schur multipliers.
Kiukas Jukka
Lahti Pekka
Pellonpaa Juha-Pekka
No associations
LandOfFree
On infinite matrices, Schur products, and operator measures does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On infinite matrices, Schur products, and operator measures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On infinite matrices, Schur products, and operator measures will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-112590