Spectral resolutions for $\sigma$-complete lattice effect algebras
Mathematica slovaca, Tome 56 (2006) no. 5, pp. 555-571
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 03G12, 81P10
@article{MASLO_2006_56_5_a6,
     author = {Pulmannov\'a, Sylvia},
     title = {Spectral resolutions for $\sigma$-complete lattice effect algebras},
     journal = {Mathematica slovaca},
     pages = {555--571},
     year = {2006},
     volume = {56},
     number = {5},
     mrnumber = {2293587},
     zbl = {1141.81007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MASLO_2006_56_5_a6/}
}
TY  - JOUR
AU  - Pulmannová, Sylvia
TI  - Spectral resolutions for $\sigma$-complete lattice effect algebras
JO  - Mathematica slovaca
PY  - 2006
SP  - 555
EP  - 571
VL  - 56
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MASLO_2006_56_5_a6/
LA  - en
ID  - MASLO_2006_56_5_a6
ER  - 
%0 Journal Article
%A Pulmannová, Sylvia
%T Spectral resolutions for $\sigma$-complete lattice effect algebras
%J Mathematica slovaca
%D 2006
%P 555-571
%V 56
%N 5
%U http://geodesic.mathdoc.fr/item/MASLO_2006_56_5_a6/
%G en
%F MASLO_2006_56_5_a6
Pulmannová, Sylvia. Spectral resolutions for $\sigma$-complete lattice effect algebras. Mathematica slovaca, Tome 56 (2006) no. 5, pp. 555-571. http://geodesic.mathdoc.fr/item/MASLO_2006_56_5_a6/

[1] BARBIERI G.-WEBER H.: Measures on clans and on MV-algebras. In: Handbook of Measure Theorу, vol II (E. Pap, ed.), Elsevier, Amsterdam, 2002, pp. 911-945 (Chap. 22). | MR | Zbl

[2] BUTNARIU D.-KLEMENT E.: Triangular-norm-based measures and their Markov kernel representation. J. Math. Anal. Appl. 162 (1991), 111-143. | MR | Zbl

[3] CHANG C. C.: Algebraic analysis of many-valued logics. Trans. Amer. Math. Soc. 88 (1958), 467-490. | MR | Zbl

[4] CHANG C. C.: A new proof of the completeness of the Lukasiewicz axioms. Trans. Amer. Math. Soc. 93 (1959), 74-80. | MR | Zbl

[5] CIGNOLI R.-D'OTTAVIANO I. M. L.-MUNDICI D.: Algebraic Foundation of Many-Valued Reasoning. Kluwer Acad. PubL, Dordrecht, 2000. | MR

[6] CHOVANEC F.-KOPKA F.: D-lattices. Internat. J. Theoret. Phys. 34 (1995), 1297-1302. | MR | Zbl

[7] DVUREČENSKIJ A.: Loomis-Sikorski theorem for $\sigma$-complete $MV$-algebras and \ell$-groups. J. Austral. Math. Soc. Ser. A 68 (2000), 261-277. | MR | Zbl

[8] DVUREČENSKIJ A.: MV-observables and MV-algebras. J. Math. Anal. Appl. 259 (2001), 413-428. | MR | Zbl

[9] DVUREČENSKIJ A.-PULMANNOVÁ S.: New Trends in Quantum Structures. Kluwer Acad. Publ./Ister Science, Dordrecht/Bratislava, 2000. | MR | Zbl

[10] DVUREČENSKIJ A.-PULMANNOVÁ S.: Conditional probability on a-MV algebras. Fuzzy Sets and Systems 155 (2005), 102-118. | MR

[11] FOULIS D. J.-BENNETT M. K.: Effect algebras and unsharp quantum logic. Found. Phys. 24 (1994), 1325-1346. | MR

[12] FOULIS D. J.: Compressible groups. Math. Slovaca 53 (2003), 433-455. | MR | Zbl

[13] FOULIS D. J.: Compressions on partially ordered abelian groups. Proc. Amer. Math.Soc. 132 (2004), 3581-3587. | MR | Zbl

[14] FOULIS D. J.: Spectral resolution in a Rickart comgroup. Rep. Math. Phys. 54 (2004), 319-340. | MR | Zbl

[15] FOULIS D. J.: Compressible groups with general comparability. Math. Slovaca. 55 (2005), 409-429. | MR | Zbl

[16] FOULIS D. J.: MV and Heyting effect algebras. Found. Phys. 30 (2000), 1687-1706. | MR

[17] GIUNTINI R.-GREULING H.: Toward a formal language for unsharp properties. Found. Phys. 19 (1989), 931-945. | MR

[18] GOODEARL K. R.: Partially Ordered Abelian Groups with Interpolation. Math. Surveys Monogr. 20, Amer. Math. Soc, Providence, RI, 1986. | MR | Zbl

[19] GUDDER S. P.: S-dominating effect algebras. Internat. J. Theoret. Phys. 37 (1998), 915-923. | MR | Zbl

[20] GUDDER S. P.: Compressible effect algebras. Rep. Math. Phys. 54 (2004), 93-114. | MR | Zbl

[21] JENČA G.: Sharp and meager elements in orthocomplete homogeneous effect algebras. Preprint, 2004 (Available from http://www.elf.stuba.sk/'jenca/preprint) | MR | Zbl

[22] JENČA G.-PULMANNOVÁ S.: Orthocomplete effect algebras. Proc Amer. Math.Soc 131 (2003), 2663-2671. | MR | Zbl

[23] JENČA G.-PULMANNOVÁ S.: Ideals and quotients in lattice ordered effect algebras. Soft Comput. 5 (2001), 376-380. | Zbl

[24] JENČA G.-RIEČANOVÁ Z.: On sharp elements in lattice ordered effect algebras. Busefal 80 (1999), 24-29.

[25] KOPKA F.-CHOVANEC F.: D-posets. Math. Slovaca 44 (1994), 21-34. | MR | Zbl

[26] MUNDICI D.: Interpretations of $AF$ $C^\ast$-algebras in Lukasziewicz sentential calculus. J. Funct. Anal. 65 (1986), 15-63. | MR

[27] MUNDICI D.: Tensor products and the Loomis-Sikorski theorem for MV-algebras. Adv. in Appl. Math. 22 (1999), 227-248. | MR | Zbl

[28] PULMANNOVÁ S.: A spectral theorem for a-MV algebras. Kybernetika 41 (2005), 361-374. | MR

[29] PULMANNOVÁ S.: Spectral resolutions in Dedekind $\sigma$-complete $\ell$-groups. J. Math. Anal. Appl. 309 (2005), 322-335. | MR | Zbl

[30] PULMANNOVÁ S.: Commutator-finite D-lattices. Order 21 (2004), 91-105. | MR | Zbl

[31] PTÁK P.-PULMANNOVÁ S.: Orthomodular Structures as Quantum Logics. Kluwer Acad. Publ./VEDA, Dordrecht/Bratislava, 1991. | MR | Zbl

[32] RIEČAN B.-NEUBRUNN T.: Integral, Measure and Ordering. Kluwer Acad. Publ./ Ister Science, Dordrecht/Bratislava, 1997. | MR | Zbl

[33] RIEČANOVÁ Z.: Generalization of blocks for D-lattices and lattice ordered effect algebras. Internat. J. Theoret. Phys. 39 (2000), 231-237. | MR | Zbl

[34] RIEČANOVÁ Z.: Smearing of states defined on sharp elements onto effect algebras. Internat. J. Theoret. Phys. 41 (2002), 1511-1524. | MR

[35] VARADARAJAN V. S.: Geometry of Quantum Theory. Springer-Verlag, New York, 1985. | MR | Zbl