caa a22 4500 463195868 CHVBK 20180406164922.0 cr unu---uuuuu 170326e20070701xx s 000 0 eng 10.1007/s10773-006-9315-9 doi (NATIONALLICENCE)springer-10.1007/s10773-006-9315-9 Niestegge Gerd Zillertalstrasse 39, D-81373, Muenchen, Germany aut Different Types of Conditional Expectation and the Lüders—von Neumann Quantum Measurement [Elektronische Daten] [Gerd Niestegge] 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 Lüders—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 Lüders—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. Springer Science+Business Media, LLC, 2007 conditional expectations nationallicence quantum measurement nationallicence operator algebras nationallicence Jordan algebras nationallicence International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/7(2007-07-01), 1823-1835 0020-7748 46:7<1823 2007 46 10773 https://doi.org/10.1007/s10773-006-9315-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10773-006-9315-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Niestegge Gerd Zillertalstrasse 39, D-81373, Muenchen, Germany aut NATIONALLICENCE 773 0- International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/7(2007-07-01), 1823-1835 0020-7748 46:7<1823 2007 46 10773 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer