Note on a construction of unbounded measures on a nonseparable Hilbert space quantum logic

Anatolij Dvurečenskij

Annales de l'I.H.P. Physique théorique (1988)

  • Volume: 48, Issue: 4, page 297-310
  • ISSN: 0246-0211

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Dvurečenskij, Anatolij. "Note on a construction of unbounded measures on a nonseparable Hilbert space quantum logic." Annales de l'I.H.P. Physique théorique 48.4 (1988): 297-310. <http://eudml.org/doc/76402>.

@article{Dvurečenskij1988,
author = {Dvurečenskij, Anatolij},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Gleason measure},
language = {eng},
number = {4},
pages = {297-310},
publisher = {Gauthier-Villars},
title = {Note on a construction of unbounded measures on a nonseparable Hilbert space quantum logic},
url = {http://eudml.org/doc/76402},
volume = {48},
year = {1988},
}

TY - JOUR
AU - Dvurečenskij, Anatolij
TI - Note on a construction of unbounded measures on a nonseparable Hilbert space quantum logic
JO - Annales de l'I.H.P. Physique théorique
PY - 1988
PB - Gauthier-Villars
VL - 48
IS - 4
SP - 297
EP - 310
LA - eng
KW - Gleason measure
UR - http://eudml.org/doc/76402
ER -

References

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  1. [1] G.D. Lugovaja, On a construction of unbounded measures on projectors of a Hilbert space. Issled. po priklad. mat., n° 10, Izd. Kazan. univ., 1984, p. 202-205 (in Russian). Zbl0664.46058
  2. [2] G.D. Lugovaja, Bilinear forms generating measures on projectors. Izv. vuzov Matem., t. 2, 1983, p. 88-88 (in Russian). Zbl0511.46061
  3. [3] A.M. Gleason, Measures on the closed subspaces of a Hilbert space. J. of Math. and Mech., t. 6, 1957, 885-894. Zbl0078.28803MR96113
  4. [4] M. Eilers, E. Horst, The theorem of Gleason for nonseparable Hilbert space. Inter. J. Theor. Phys., t. 13, 1975, p. 419-424. Zbl0345.46021MR389054
  5. [5] G.D. Lugovaja, A.N. Sherstnev, On the Gleason theorem for unbounded measures. Izv. vuzov Matem., t. 12, 1980, p. 30-32 (in Russian). Zbl0483.46042MR606673
  6. [6] A. Dvurečenskij, Generalization of Maeda's theorem. Inter. J. Theor. Phys., t. 25, 1986, p. 1117-1124. Zbl0618.46053MR868372
  7. [7] S. Ulam, Zur Masstheorie in der allgemeinen Mengelehre. Fund. Math., t. 16, 1930, p. 140-150. JFM56.0920.04
  8. [8] A. Dvurečenskij, Gleason theorem for signed measures with infinite values. Math. Slovaca, t. 35, 1985, p. 319-325. Zbl0584.46053MR820628
  9. [9] P.R. Halmos, Introduction to Hilbert space and the theory of spectral multiplicity, New York, 1951. Zbl0045.05702MR45309
  10. [10] K. Kuratowski, A. Mostowski, Set theory, Izd. Mir, Moscow, 1970 (in Russian). Zbl0204.31301MR268045
  11. [11] S.P. Gudder, Inner product spaces. Amer. Math. Monthly, t. 81, 1974, p. 29-36. Zbl0279.46013MR331027
  12. [12] B. Simon, A canonical decomposition for quadratic forms with application to monotone convergence theorems. J. Funct. Anal., t. 28, 1978, p. 377-385. Zbl0413.47029MR500266

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