Orthogonality spaces and atomistic orthocomplemented lattices

Jarmila Hedlíková; Sylvia Pulmannová

Czechoslovak Mathematical Journal (1991)

  • Volume: 41, Issue: 1, page 8-23
  • ISSN: 0011-4642

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Hedlíková, Jarmila, and Pulmannová, Sylvia. "Orthogonality spaces and atomistic orthocomplemented lattices." Czechoslovak Mathematical Journal 41.1 (1991): 8-23. <http://eudml.org/doc/13894>.

@article{Hedlíková1991,
author = {Hedlíková, Jarmila, Pulmannová, Sylvia},
journal = {Czechoslovak Mathematical Journal},
keywords = {orthogonality spaces; atomistic orthocomplemented lattices; lattice of closed subspaces of a generalized inner product space; minimal dependence; minimal superposition; atomic exchange property},
language = {eng},
number = {1},
pages = {8-23},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Orthogonality spaces and atomistic orthocomplemented lattices},
url = {http://eudml.org/doc/13894},
volume = {41},
year = {1991},
}

TY - JOUR
AU - Hedlíková, Jarmila
AU - Pulmannová, Sylvia
TI - Orthogonality spaces and atomistic orthocomplemented lattices
JO - Czechoslovak Mathematical Journal
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 41
IS - 1
SP - 8
EP - 23
LA - eng
KW - orthogonality spaces; atomistic orthocomplemented lattices; lattice of closed subspaces of a generalized inner product space; minimal dependence; minimal superposition; atomic exchange property
UR - http://eudml.org/doc/13894
ER -

References

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  1. I. Amemiya H. Araki, 10.2977/prims/1195195769, Publ. Research Inst. Math. Sci. Kyoto Univ. Series A 2 (1966) 423-427. (1966) Zbl0177.16103MR0213266DOI10.2977/prims/1195195769
  2. G. Birkhoff, Lattice theory, Coll. Publ. 25, Amer. Math. Soc., Providence, 3rd ed., 1967. (1967) Zbl0153.02501MR0227053
  3. G. Cattaneo G. Marino, 10.1007/BF00417459, Letters in Math. Physics 11 (1986) 15-20. (1986) Zbl0601.46026MR0824671DOI10.1007/BF00417459
  4. A. Dvurečenskij, 10.1007/BF00398592, Letters in Math. Physics 15 (1988) 231 - 235. (1988) Zbl0661.46019MR0948357DOI10.1007/BF00398592
  5. A. Dvurečenskij, 10.1007/BF00420009, Letters in Math. Physics 17 (1989) 19-24. (1989) Zbl0696.46023MR0990578DOI10.1007/BF00420009
  6. P. D. Finch, 10.1017/S0004972700041678, Bull. Austral. Math. Soc. 2 (1970) 125-128. (1970) Zbl0179.03401MR0262122DOI10.1017/S0004972700041678
  7. D. J. Foulis C. H. Randall, 10.1016/0097-3165(71)90040-9, J. Combinatorial Theory Ser. A 11 (1971) 157-162. (1971) Zbl0272.06008MR0280420DOI10.1016/0097-3165(71)90040-9
  8. R. Goldblatt, Orthomodularity is not elementary, Journal Symbolic Logic 49 (1984)401-404. (1984) Zbl0593.03042MR0745368
  9. H. Gross H. A. Keller, 10.1007/BF01168586, Manuscripta Math. 23 (1977) 67-90. (1977) Zbl0365.46023MR0482101DOI10.1007/BF01168586
  10. S. P. Gudder, 10.1007/BF02412750, Internat. J. Theoret. Physics 3 (1970) 99-108. (1970) MR0416297DOI10.1007/BF02412750
  11. S. Gudder, 10.2307/2318908, Amer. Math. Monthly 81 (1974) 29-36. (1974) Zbl0279.46013MR0331027DOI10.2307/2318908
  12. S. Gudder, 10.2307/2319847, Amer. Math. Monthly 82 (1975) 251-252. (1975) Zbl0305.46033MR0420234DOI10.2307/2319847
  13. S. Gudder S. Holland, Second correction to: „Inner product spaces", Amer. Math. Monthly 82 (1975) 818. (1975) Zbl0329.46017MR0380374
  14. W. Guz, Filter theory and covering law, Ann. Inst. H. Poincarè Sec. A Phys. Thèor. 29 (1978) 357-378. (1978) Zbl0398.03052MR0525388
  15. J. Hamhalter P. Pták, 10.1112/blms/19.3.259, Bull. London Math. Soc. 19 (1987) 259-263. (1987) Zbl0601.46027MR0879514DOI10.1112/blms/19.3.259
  16. L. Iturrioz, Orthomodular ordered sets and orthogonal closure spaces, Portugal. Math. 39 (1980) 477-488. (1980) Zbl0559.06005MR0776257
  17. G. Kalmbach, Orthomodular lattices, Academic Press, London, 1983. (1983) Zbl0528.06012MR0716496
  18. M. D. MacLaren, 10.2140/pjm.1964.14.597, Pacific J. Math. 14 (1964) 597-612. (1964) Zbl0122.02201MR0163860DOI10.2140/pjm.1964.14.597
  19. F. Maeda S. Maeda, Theory of symmetric lattices, Springer-Verlag, Berlin 1970. (1970) Zbl0219.06002MR0282889
  20. C. Piron, Foundations of quantum physics, Benjamin, Reading, Massachusetts, 1976. (1976) Zbl0333.46050MR0673578
  21. R. Piziak, 10.1017/S1446788700013161, J. Austral. Math. Soc. 15 (1973) 265-269. (1973) Zbl0271.15013MR0325657DOI10.1017/S1446788700013161
  22. S. Pulmannová, Superpositions of states and a representation theorem, Ann. Inst. H. Poincarè Sec. A Phys. Thèor. 32 (1980) 351-360. (1980) Zbl0453.03066MR0594634
  23. S. Pulmannová, 10.1063/1.527045, J. Math. Physics 27 (1986) 1791-1795. (1986) Zbl0638.03060MR0844219DOI10.1063/1.527045
  24. V. S. Varadarajan, Geometry of quantum theory, 2nd ed., Springer-Verlag, New York, 1985. (1985) Zbl0581.46061MR0805158

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