Geodesic
Order properties of splitting subspaces in an inner product space
Mathematica slovaca, Tome 54 (2004) no. 2, pp. 119-126
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 03G12, 06C15, 46C05, 81P10 
@article{MASLO_2004_54_2_a1,
     author = {Pt\'ak, Pavel and Weber, Hans},
     title = {Order properties of splitting subspaces in an inner product space},
     journal = {Mathematica slovaca},
     pages = {119--126},
     year = {2004},
     volume = {54},
     number = {2},
     mrnumber = {2074209},
     zbl = {1065.03048},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MASLO_2004_54_2_a1/}
}
TY  - JOUR
AU  - Pták, Pavel
AU  - Weber, Hans
TI  - Order properties of splitting subspaces in an inner product space
JO  - Mathematica slovaca
PY  - 2004
SP  - 119
EP  - 126
VL  - 54
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MASLO_2004_54_2_a1/
LA  - en
ID  - MASLO_2004_54_2_a1
ER  - 
%0 Journal Article
%A Pták, Pavel
%A Weber, Hans
%T Order properties of splitting subspaces in an inner product space
%J Mathematica slovaca
%D 2004
%P 119-126
%V 54
%N 2
%U http://geodesic.mathdoc.fr/item/MASLO_2004_54_2_a1/
%G en
%F MASLO_2004_54_2_a1
Pták, Pavel; Weber, Hans. Order properties of splitting subspaces in an inner product space. Mathematica slovaca, Tome 54 (2004) no. 2, pp. 119-126. http://geodesic.mathdoc.fr/item/MASLO_2004_54_2_a1/

[1] AMEMIYA L.-ARAKI H.: A remark on Pirorís paper. Publ. Res. Inst. Math. Sci. 2 (1966), 423-427. | MR

[2] CHETCUTI E.-DVUREČENSKIJ A.: A finitely additive state criterion for the completeness of inner product spaces. Lett. Math. Phys. 64 (2003), 221-227. | MR | Zbl

[3] DVUREČENSKIJ A.: A new algebraic criterion for completeness of inner product spaces. Lett. Math. Phys. 58 (2001), 205-208. | MR | Zbl

[4] DVUREČENSKIJ A.: Gleason's Theorem and Applications. Kluwer Acad. Publ., Dordrecht-Boston-London, 1993. | MR

[5] DVUREČENSKIJ A.-PTÁK P.: Quantum logics with the Riesz Interpolation Property. Math. Nachr. 271 (2004) (To appear). | MR | Zbl

[6] DVUREČENSKIJ A.-NEUBRUNN T.-PULMANNOVÁ S.: Finitely additive states and completeness of inner product spaces. Found. Phys. 20 (1990), 1091-1102. | MR | Zbl

[7] FRENICHE F.: The Vitali-Hahn-Sachs theorem for Boolean algebras with the subsequential interpolation property. Proc. Amer. Math. Soc. 92 (1984), 312-366. | MR

[8] GOODEARL K. R.: Partially ordered Abelian groups with interpolation. Math. Surveys Monogr. 20, Amer. Math. Soc, Providence, RI, 1986. | MR | Zbl

[9] HAMHALТER J.-PТÁK P.: A completeness criterion for inner product spaces. Bull. London Math. Soc. 19 (1987), 259-263. | MR

[10] HARDING J.: Decompositions in quantum logics. Тrans. Amer. Math. Soc. 348 (1996), 1839-1862. | MR

[11] HARDING J.: Regularity in quantum logics. Internat. J. Тheoret. Phys. 37 (1998), 1173-1212. | MR

[12] HOLLAND S. S. JR.: Orthomodularity in infinite dimensions - a theorem of M. Solér. Bull. Amer. Math. Soc. 32 (1995), 205-234. | MR | Zbl

[13] KALMBACH G.: Orthomodular Lattices. Academic Press, London, 1983. | MR | Zbl

[14] KELLER H.: Ein nicht-klassischer Hilbertischen Raum. Math. Z. 272 (1980), 42-49. | MR

[15] MAEDA F.-MAEDA S.: Theory of Symmetric Lattices. Springer-Verlag, Berlin, 1970. | MR | Zbl

[16] PIZIAK R.: Lattice theory, quadratic spaces, and quantum proposition systems. Found. Phys. 20 (1990), 651-665. | MR

[17] PТÁK P.-PULMANNOVÁ S.: Orthomodular Structures as Quantum Logics. Kluwer Acad. Publ., Dordrecht, 1991. | MR

[18] PTÁK P.-WEBER H.: Lattice properties of subspace families in an inner product space. Proc. Amer. Math. Soc. 129 (2001), 2111-2117. | MR | Zbl

[19] SOLER M.: Characterization of Hilbert space by orthomodular spaces. Comm. Algebra 23 (1995), 219-243. | MR

[20] VARADARAJAN V.: Geometry of Quantum Theory I; II. Van Nostrand, Princeton, 1968; 1970.

[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. | MR