Decomposition theorems in orthomodular posets: The problem of uniqueness

De Simone, Anna

doi:10.1090/S0002-9939-98-04380-9

Decomposition theorems in orthomodular posets: The problem of uniqueness
HTML articles powered by AMS MathViewer

by Anna De Simone PDF

Proc. Amer. Math. Soc. 126 (1998), 2919-2926 Request permission

Abstract:

We provide some conditions which are equivalent to the uniqueness of Hewitt-Yosida-type decomposition and Lebesgue-type decomposition for real valued additive functions defined on orthomodular posets.

References

Ladislav Beran, Orthomodular lattices, Academia [Publishing House of the Czech Academy of Sciences], Prague, 1984. Algebraic approach. MR 785005
Anna Bruna D’Andrea and Paolo De Lucia, The Lebesgue decomposition theorem on an orthomodular lattice, Rend. Circ. Mat. Palermo (2) Suppl. 28 (1992), 379–386. Measure theory (Oberwolfach, 1990). MR 1183063
Anna Bruna D’Andrea and Paolo De Lucia, On the Lebesgue decomposition of a function relative to a $p$-ideal of an orthomodular lattice, Math. Slovaca 41 (1991), no. 4, 423–430. MR 1149048
Anna Bruna D’Andrea, Paolo De Lucia, and Pedro Morales, The Lebesgue decomposition theorem and the Nikodým convergence theorem on an orthomodular poset, Atti Sem. Mat. Fis. Univ. Modena 39 (1991), no. 1, 73–94. MR 1111759
Paolo De Lucia and Anatolij Dvurečenskij, Decompositions of Riesz space-valued measures on orthomodular posets, Tatra Mt. Math. Publ. 2 (1993), 229–239. MR 1251058
Paolo De Lucia and Pedro Morales, Noncommutative decomposition theorems in Riesz spaces, Proc. Amer. Math. Soc. 120 (1994), no. 1, 193–202. MR 1203982, DOI 10.1090/S0002-9939-1994-1203982-0
Anatolij Dvurečenskij, Paolo De Lucia, and Endre Pap, On a decomposition theorem and its applications, Math. Japon. 44 (1996), no. 1, 145–164. MR 1402810
Gudrun Kalmbach, Orthomodular lattices, London Mathematical Society Monographs, vol. 18, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1983. MR 716496
Pavel Pták and Sylvia Pulmannová, Kvantové logiky, VEDA, Vydavatel′stvo Slovenskej Akadémie Vied, Bratislava, 1989 (Slovak, with English and Russian summaries). MR 1176313
Gottfried T. Rüttimann, Decomposition of cones of measures, Atti Sem. Mat. Fis. Univ. Modena 38 (1990), no. 2, 267–279. MR 1076452
Gottfried T. Rüttimann, Weakly purely finitely additive measures, Canad. J. Math. 46 (1994), no. 4, 872–885. MR 1289065, DOI 10.4153/CJM-1994-049-1
G. T. Rüttimann and Chr. Schindler, The Lebesgue decomposition of measures on orthomodular posets, Quart. J. Math. Oxford Ser. (2) 37 (1986), no. 147, 321–345. MR 854631, DOI 10.1093/qmath/37.3.321
Hans Weber, Lattice uniformities and modular functions on orthomodular lattices, Order 12 (1995), no. 3, 295–305. MR 1361614, DOI 10.1007/BF01111744