Regular Gleason Measures and Generalized Effect Algebras

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• 作者：Anatolij Dvure?enskij ; Ji?í Janda
• 关键词：Hilbert space ; Measure ; Regular measure ; σ ; additive measure ; Gleason measure ; Generalized effect algebra ; Bilinear form ; Singular bilinear form ; Regular bilinear form ; Monotone convergence
• 刊名：International Journal of Theoretical Physics
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：54
• 期：12
• 页码：4313-4326
• 全文大小：351 KB
• 参考文献：1.Fichtengol’c, G.M.: Kurs differencial’nogo i integral’nogo is?islenia. Fizmatgiz, Moskva (1962). (in Russian)
  2.Dorofeev, S.V., Sherstnev, A.N.: Frame-type functions and their applications, Izv. vuzov matem. No. 4 (1990), 23-9 (in Russian). English translation: Sov. Math. 34(4), 25-1 (1990)MATH MathSciNet
  3.Dvure?enskij, A.: Signed states on a logic. Math. Slovaca 28, 33-0 (1978)MATH MathSciNet
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  5.Dvure?enskij, A.: Gleason’s Theorem and its Applications, Mathematics and its Applications, vol. 60. Kluwer Acad. Publ., Dordrecht/Ister Science, Bratislava (1993)CrossRef
  6.Dvure?enskij, A., Janda, J.: On bilinear forms from the point of view of generalized effect algebras. Found. Phys. 43, 1136-152 (2013). doi:10.-007/?s10701-013-9736-2 MATH MathSciNet CrossRef ADS
  7.Dvure?enskij, A., Pulmannová, S.: New Trends in Quantum Structures. Kluwer Academic Publ., Dordrecht, Ister Science, Bratislava, 541 + xvi pp (2000)
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  10.Halmos, P.R. Introduction to Hilbert Space and the Theory of Spectral Multiplicity, 2nd ed. Chelsea Publ. Co., New York (1957)
  11.Lugovaya, G.D.: Bilinear forms defining measures on projectors. Izv. Vyssh. Uchebn. Zaved., Mat. No. 2 249 (1983), 88-8 (in Russian). English translation: Sov. Math. 27, 102-02 (1983)MATH
  12.Lugovaya, G.D.: On a construction of unbounded measures on projectors of Hilbert space. Issled. po priklad. matem., Izdat. Kazan Univ. (1984), 202-05 (in Russian). English translation: J. Sov. Math. 44(5), 711-13 (1984)
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  14.Rie?anová, Z., Zajac, M., Pulmannová, S.: Effect algebras of positive linear operators densely defined on Hilbert spaces. Rep. Math. Phys. 68, 261-70 (2011)MATH MathSciNet CrossRef ADS
  15.Sherstnev, A.N.: On a notion of a charge in noncommutative scheme of measure theory. In: Veroj. metod i kibern., Kazan, No. 10-11, pp. 68-2 (in Russian) (1974)
  16.Simon, B.: A canonical decomposition for quadratic forms with applications for monotone convergence theorems. J. Funct. Analysis 28, 377-85 (1978)MATH CrossRef
  
• 作者单位：Anatolij Dvure?enskij (1) (2)
  Ji?í Janda (3)
  
  1. Mathematical Institute, Slovak Academy of Sciences, ?tefánikova 49, SK-814 73, Bratislava, Slovakia
  2. Department of Algebra and Geometry, Palacky University, 17. listopadu 12, CZ-771 46, Olomouc, Czech Republic
  3. Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlá?ská 267/2, CZ-611 37, Brno, Czech Republic
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Physics
  Quantum Physics
  Elementary Particles and Quantum Field Theory
  Mathematical and Computational Physics
  
• 出版者：Springer Netherlands
• ISSN：1572-9575

文摘

We study measures, finitely additive measures, regular measures, and σ-additive measures that can attain even infinite values on the quantum logic of a Hilbert space. We show when particular classes of non-negative measures can be studied in the frame of generalized effect algebras. Keywords Hilbert space Measure Regular measure σ-additive measure Gleason measure Generalized effect algebra Bilinear form Singular bilinear form Regular bilinear form Monotone convergence