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Spectral representation of infimum of bounded quantum observables

J. Math. Phys. 50, 113501 (2009); doi:10.1063/1.3253609

Published 2 November 2009

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Shen Jun1,2 and Wu Junde1
1Department of Mathematics, Zhejiang University, Hangzhou 310027, People's Republic of China
2Department of Mathematics, Anhui Normal University, Wuhu 241003, People's Republic of China
In 2006, Gudder [Math. Slovaca 56, 573 (2006)] introduced a logic order [curly precedes, eq] on bounded quantum observable set S(H). In 2007, Pulmannova and Vincekova [Math Slovaca 57, 589 (2007)] proved that for each subset [script D] of S(H), the infimum of [script D] exists with respect to the logic order [curly precedes, eq]. In 2008, Liu and Wu [J. Math. Phys. 49, 073521 (2008)] found a representation of the infimum A[logical and]B for A,B[is-an-element-of]S(H), and by using the limit methods, they gave out a representation for the infimum of [script D]. But, that representation is complicated. In this paper, we present a simpler spectral representation for the infimum of [script D] with respect to the logic order [curly precedes, eq]. ©2009 American Institute of Physics
History: Received 8 June 2009; accepted 16 September 2009; published 2 November 2009
Permalink: http://link.aip.org/link/?JMAPAQ/50/113501/1
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KEYWORDS and PACS

Keywords
PACS
  • 03.65.Fd
    Algebraic methods in quantum mechanics
  • 02.10.Ab
    Logic and set theory
  • YEAR: 2009

PUBLICATION DATA

ISSN:
0022-2488 (print)   1089-7658 (online)
Publisher:
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REFERENCES (10)
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  1. S. Gudder, Math. Slovaca 56, 573 (2006).
  2. R. Kadison, Proc. Am. Math. Soc. 2, 505 (1951).
  3. T. Moreland and S. Gudder, Linear Algebr. Appl. 286, 1 (1999).
  4. S. Gudder, J. Math. Phys. 37, 2637 (1996).
  5. T. Ando, Analytic and Geometric Inequalities and Applications (Kluwer, Dordrecht, 1999), Vol. 478, p. 1.
  6. H. K. Du, C. Y. Deng, and Q. H. Li, Sci. China, Ser. A: Math., Phys., Astron. 49, 545 (2006).
  7. S. Pulmannova and E. Vincekova, Math Slovaca 57, 589 (2007).
  8. W. H. Liu and J. D. Wu, J. Math. Phys. 49, 073521 (2008).
  9. X. M. Xu, H. K. Du, and X. C. Fang, J. Math. Phys. 50, 033502 (2009).
  10. W. H. Liu and J. D. Wu, J. Math. Phys. 50, 083513 (2009).

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