Regular Gleason Measures and Generalized Effect Algebras

被引：0
作者：
Anatolij Dvurečenskij
Jiří Janda
机构：
[1] Mathematical Institute,Department of Algebra and Geometry
[2] Slovak Academy of Sciences,Department of Mathematics and Statistics, Faculty of Science
[3] Palacký University,undefined
[4] Masaryk University,undefined
来源：
International Journal of Theoretical Physics | 2015年 / 54卷
关键词：
Hilbert space; Measure; Regular measure; -additive measure; Gleason measure; Generalized effect algebra; Bilinear form; Singular bilinear form; Regular bilinear form; Monotone convergence;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
引用
收藏
页码：4313 / 4326
页数：13
相关论文
共 16 条
  • [1] Dorofeev SV(1990)Frame-type functions and their applications, Izv. vuzov matem. No. 4 (1990), 23–29 (in Russian) English translation: Sov. Math. 34 25-31
  • [2] Sherstnev AN(1978)Signed states on a logic Math. Slovaca 28 33-40
  • [3] Dvurečenskij A(1987)Converse of the Eilers-Horst theorem Inter. J. Theor. Phys. 26 609-612
  • [4] Dvurečenskij A(2013)On bilinear forms from the point of view of generalized effect algebras Found. Phys. 43 1136-1152
  • [5] Dvurečenskij A(1994)Effect algebras and unsharp quantum logics Found. Phys. 24 1331-1352
  • [6] Janda J(1957)Measures on the closed subspaces of a Hilbert space J. Math. Mech. 6 885-893
  • [7] Foulis DJ(1983)Bilinear forms defining measures on projectors. Izv. Vyssh. Uchebn. Zaved., Mat. No. 2 249 (1983), 88–88 (in Russian) English translation: Sov. Math. 27 102-102
  • [8] Bennett MK(1980)On the Gleason theorem for unbounded measures, Izv. vuzov matem. No. 2 (1980), 30–32 (in Russian) English translation: Sov. Math. 24 35-38
  • [9] Gleason AM(2011)Effect algebras of positive linear operators densely defined on Hilbert spaces Rep. Math. Phys. 68 261-270
  • [10] Lugovaya GD(1978)A canonical decomposition for quadratic forms with applications for monotone convergence theorems J. Funct. Analysis 28 377-385
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