Abstract
In this chapter we discuss some common examples of semispectral measures and their natural dilations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Sikorski, R.: On the inducing of homomorphisms by mappings. Fundam. Math. 36, 7–22 (1949)
Akhiezer, N.I., Glazman, I.M.: Theory of Linear Operators in Hilbert Space. Dover Publications Inc., New York (1993) (Translated from the Russian and with a preface by Merlynd Nestell, Reprint of the 1961 and 1963 translations, Two volumes bound as one)
Varadarajan, V.S.: Geometry of Quantum Theory, vol. 2. Springer, New York (1985)
Taylor, B., Mohr, P.: The NIST Reference on Constants, Units, and Uncertainty. http://physics.nist.gov/cuu/index.html
Douglas, R.G.: Banach Algebra Techniques in Operator Theory. Pure and Applied Mathematics, vol. 49, Academic Press, New York (1972)
Holevo, A.S.: Statistical Structure of Quantum Theory. Lecture Notes in Physics, vol. 67. Monographs. Springer, Berlin (2001)
Halmos, P.R.: Measure Theory, 4th edn. Springer, Berlin (1988) (Reprint of the 1950 edition)
Dunford, N., Schwartz, J.T.: Linear Operators. Part I. Wiley Classics Library. Wiley, New York (1988) (Reprint of the 1958 original, A Wiley-Interscience Publication)
Kiukas, J., Lahti, P., Ylinen, K.: Semispectral measures as convolutions and their moment operators. J. Math. Phys. 49(11), 112103, 6 (2008)
Carmeli, C., Heinonen, T., Toigo, A.: Position and momentum observables on \({\mathbb{R}}\) and on \({\mathbb{R}}^3\). J. Math. Phys. 45(6), 2526–2539 (2004)
Kiukas, J., Lahti, P., Ylinen, K.: Normal covariant quantization maps. J. Math. Anal. Appl. 319(2), 783–801 (2006)
Holevo, A.S.: Covariant measurements and uncertainty relations. Rep. Math. Phys. 16(3), 385–400 (1979)
Werner, R.: Quantum harmonic analysis on phase space. J. Math. Phys. 25(5), 1404–1411 (1984)
Cassinelli, G., De Vito, E., Toigo, A.: Positive operator valued measures covariant with respect to an irreducible representation. J. Math. Phys. 44(10), 4768–4775 (2003)
Kiukas, J., Lahti, P., Ylinen, K.: Phase space quantization and the operator moment problem. J. Math. Phys. 47(7), 072104, 18 (2006)
Riesz, F., Nagy, B.S.: Functional Analysis. Dover Books on Advanced Mathematics. Dover Publications Inc., New York (1990) (Translated from the second French edition by Leo F. Boron, Reprint of the 1955 original)
Hytönen, T., Pellonpää, J.-P., Ylinen, K.: Positive sesquilinear form measures and generalized eigenvalue expansions. J. Math. Anal. Appl. 336(2), 1287–1304 (2007)
Pellonpää, J.-P.: Complete characterization of extreme quantum observables in infinite dimensions. J. Phys. A 44(8), 085304, 12 (2011)
Dixmier, J.:. Von Neumann Algebras. North-Holland Mathematical Library, vol. 27. North-Holland Publishing Co., Amsterdam (1981) (Translated from the second French edition by F. Jellett)
Pellonpää, J.-P.: Quantum instruments: II. Measurement theory. J. Phys. A 46(2), 025303, 15 (2013)
Pellonpää, J.-P., Tukiainen, M.: Minimal normal measurement models of quantum instruments. arXiv:1509.08886
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Busch, P., Lahti, P., Pellonpää, JP., Ylinen, K. (2016). Positive Operator Measures: Examples. In: Quantum Measurement. Theoretical and Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-43389-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-43389-9_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-43387-5
Online ISBN: 978-3-319-43389-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)