Quantum Instruments and Related Transformation Valued Functions |
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Authors: | Kari Ylinen |
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Affiliation: | (1) Department of Mathematics, University of Turku, 20014 Turku, Finland |
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Abstract: | The notion of an instrument in the quantum theory of measurement is studied in the context of transformation valued linear maps on von Neumann algebras and their *-subalgebras. An extension theorem is proved which yields among other things characterizations of the Fourier transforms of instruments and their noncommutative analogues. As an application, an ergodic type theorem for a general class of transformation valued functions on a locally compact group is obtained. |
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Keywords: | Quantum theory of measurement Instrument von Neumann algebra Completely positive Positive-definite Fourier transform Weakly compact operator Group C *-algebra |
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