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Journal of Mathematical Physics / Volume 52 / Issue 12 / ARTICLES / Quantum Mechanics (General and Nonrelativistic)

J. Math. Phys. 52, 122101 (2011); http://dx.doi.org/10.1063/1.3671331 (6 pages)

On the supremum and infimum of bounded quantum observables

Long Long1 and Shifang Zhang2

1School of Mathematics, Central South University, Changsha 410075, People's Republic of China
2Department of Mathematics, Fujian Normal University, Fuzhou 350007, People's Republic of China

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(Received 16 May 2011; accepted 28 November 2011; published online 20 December 2011)

Let S(H) be the set of all bounded self-adjoint linear operators on a complex Hilbert space H. In 2006, Gudder [Math. Slovaca 56, 573 (2006)] introduced a new order ≼ on S(H). Since then, the existence conditions and representations of the supremum and infimum of two elements in S(H) with respect to the order ≼ have been intensively studied. Specifically, Li and Sun [J. Math. Phys. 50, 122107 (2009)]10.1063/1.3272542 obtained simpler representations of A ∧ P and A ∨ P, where A∈S(H) and P is an orthogonal projection on H. In this note, we present more intuitive and concise results on A ∨ P and extend the results of Li and Sun to more general cases. Moreover, some applications of our results are given to show that our results are easier to deal with.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. MAIN RESULTS

ERRATUM

  1. Erratum: “On the supremum and infimum of bounded quantum observables” [J. Math. Phys. 52, 122101 (2011)]
    Long Long et al.
    J. Math. Phys. 53, 019902 (2012)JMAPAQ000053000001019902000001

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KEYWORDS and PACS

Keywords

Hilbert spaces, mathematical operators, quantum theory

PACS

  • 03.65.Ta

    Foundations of quantum mechanics; measurement theory

  • 03.65.Aa

    Quantum systems with finite Hilbert space

  • 02.30.Tb

    Operator theory

  • 03.65.Fd

    Algebraic methods

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3671331

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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