Czechoslovak Mathematical Journal, Vol. 57, No. 2, pp. 737-746, 2007

Group-valued measures on coarse-grained
quantum logics

Anna De Simone, Pavel Ptak

Anna De Simone, Dipartimento di Matematica, e Statistica, Universita degli Studi, "Federico II" di Napoli, 80126 Napoli, Italy, e-mail: annades@unina.it; Pavel Ptak, Czech Technical University, Faculty of Electrical Eng., Department of Mathematics, 166 27 Prague 6, Czech Republic, e-mail: ptak@math.feld.cvut.cz

Abstract: In \cite{GudMar} it was shown that a (real) signed measure on a cyclic coarse-grained quantum logic can be extended, as a signed measure, over the entire power algebra. Later (\cite{Ovchi}) this result was re-proved (and further improved on) and, moreover, the non-negative measures were shown to allow for extensions as non-negative measures. In both cases the proof technique used was the technique of linear algebra. In this paper we further generalize the results cited by extending group-valued measures on cyclic coarse-grained quantum logics (or non-negative group-valued measures for lattice-ordered groups). Obviously, the proof technique is entirely different from that of the preceding papers. In addition, we provide a new combinatorial argument for describing all atoms of cyclic coarse-grained quantum logics.

Keywords: coarse-grained quantum logic, group-valued measure, measure extension

Classification (MSC 2000): 06C15, 81P10, 28A99, 28A55


Full text available as PDF (smallest), as compressed PostScript (.ps.gz) or as raw PostScript (.ps).

Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.
Subscribers of Springer need to access the articles on their site, which is http://www.springeronline.com/10587.


[Previous Article] [Next Article] [Contents of This Number] [Contents of Czechoslovak Mathematical Journal]