Physics – Mathematical Physics
Scientific paper
2010-01-21
2007 International Journal of Theoretical Physics 46, 1823 - 1835
Physics
Mathematical Physics
10 pages, the original publication is available at http://www.springerlink.com
Scientific paper
10.1007/s10773-006-9315-9
In operator algebra theory, a conditional expectation is usually assumed to be a projection map onto a sub-algebra. In the paper, a further type of conditional expectation and an extension of the Lueders - von Neumann measurement to observables with continuous spectra are considered; both are defined for a single operator and become a projection map only if they exist for all operators. Criteria for the existence of the different types of conditional expectation and of the extension of the Lueders - von Neumann measurement are presented, and the question whether they coincide is studied. All this is done in the general framework of Jordan operator algebras. The examples considered include the type I and type II operator algebras, the standard Hilbert space model of quantum mechanics, and a no-go result concerning the conditional expectation of observables that satisfy the canonical commutator relation.
Niestegge Gerd
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