Order properties of splitting subspaces in an inner product space

Pavel Pták; Hans Weber

Mathematica Slovaca (2004)

  • Volume: 54, Issue: 2, page 119-126
  • ISSN: 0232-0525

How to cite

top

Pták, Pavel, and Weber, Hans. "Order properties of splitting subspaces in an inner product space." Mathematica Slovaca 54.2 (2004): 119-126. <http://eudml.org/doc/32144>.

@article{Pták2004,
author = {Pták, Pavel, Weber, Hans},
journal = {Mathematica Slovaca},
keywords = {inner product space; splitting subspace; orthomodular poset},
language = {eng},
number = {2},
pages = {119-126},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Order properties of splitting subspaces in an inner product space},
url = {http://eudml.org/doc/32144},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Pták, Pavel
AU - Weber, Hans
TI - Order properties of splitting subspaces in an inner product space
JO - Mathematica Slovaca
PY - 2004
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 54
IS - 2
SP - 119
EP - 126
LA - eng
KW - inner product space; splitting subspace; orthomodular poset
UR - http://eudml.org/doc/32144
ER -

References

top
  1. AMEMIYA L.-ARAKI H., A remark on Pirorís paper, Publ. Res. Inst. Math. Sci. 2 (1966), 423-427. (1966) MR0213266
  2. CHETCUTI E.-DVUREČENSKIJ A., A finitely additive state criterion for the completeness of inner product spaces, Lett. Math. Phys. 64 (2003), 221-227. Zbl1041.46014MR2009260
  3. DVUREČENSKIJ A., A new algebraic criterion for completeness of inner product spaces, Lett. Math. Phys. 58 (2001), 205-208. Zbl1005.46012MR1892920
  4. DVUREČENSKIJ A., Gleason's Theorem and Applications, Kluwer Acad. Publ., Dordrecht-Boston-London, 1993. (1993) MR1256736
  5. DVUREČENSKIJ A.-PTÁK P., Quantum logics with the Riesz Interpolation Property, Math. Nachr. 271 (2004) (To appear). Zbl1051.03052MR2068880
  6. DVUREČENSKIJ A.-NEUBRUNN T.-PULMANNOVÁ S., Finitely additive states and completeness of inner product spaces, Found. Phys. 20 (1990), 1091-1102. (1990) Zbl0752.46008MR1078957
  7. FRENICHE F., The Vitali-Hahn-Sachs theorem for Boolean algebras with the subsequential interpolation property, Proc. Amer. Math. Soc. 92 (1984), 312-366. (1984) MR0759653
  8. GOODEARL K. R., Partially ordered Abelian groups with interpolation, Math. Surveys Monogr. 20, Amer. Math. Soc, Providence, RI, 1986. (1986) Zbl0589.06008MR0845783
  9. HAMHALТER J.-PТÁK P., A completeness criterion for inner product spaces, Bull. London Math. Soc. 19 (1987), 259-263. (1987) MR0879514
  10. HARDING J., Decompositions in quantum logics, Тrans. Amer. Math. Soc. 348 (1996), 1839-1862. (1996) MR1340177
  11. HARDING J., Regularity in quantum logics, Internat. J. Тheoret. Phys. 37 (1998), 1173-1212. (1998) MR1626771
  12. HOLLAND S. S. JR., Orthomodularity in infinite dimensions - a theorem of M. Solér, Bull. Amer. Math. Soc. 32 (1995), 205-234. (1995) Zbl0856.11021MR1307904
  13. KALMBACH G., Orthomodular Lattices, Academic Press, London, 1983. (1983) Zbl0528.06012MR0716496
  14. KELLER H., Ein nicht-klassischer Hilbertischen Raum, Math. Z. 272 (1980), 42-49. (1980) MR0576294
  15. MAEDA F.-MAEDA S., Theory of Symmetric Lattices, Springer-Verlag, Berlin, 1970. (1970) Zbl0219.06002MR0282889
  16. PIZIAK R., Lattice theory, quadratic spaces, and quantum proposition systems, Found. Phys. 20 (1990), 651-665. (1990) MR1067796
  17. PТÁK P.-PULMANNOVÁ S., Orthomodular Structures as Quantum Logics, Kluwer Acad. Publ., Dordrecht, 1991. (1991) MR1176314
  18. PTÁK P.-WEBER H., Lattice properties of subspace families in an inner product space, Proc. Amer. Math. Soc. 129 (2001), 2111-2117. Zbl0968.03077MR1825924
  19. SOLER M., Characterization of Hilbert space by orthomodular spaces, Comm. Algebra 23 (1995), 219-243. (1995) MR1311786
  20. VARADARAJAN V., Geometry of Quantum Theory I; II, Van Nostrand, Princeton, 1968; 1970. (1968) 
  21. WEBER H., Compactness in spaces of group-valued contents, the Vitali-Hahn-Sachs theorem and Nikodym boundedness theorem, Rocky Mountain J. Math. 16 (1986), 253-275. (1986) MR0843053

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.