Unconditional convergence in lattice groups with respect to ideals

• Autorzy: Boccuto A. , Dimitriou X. , Papanastassiou N.
• Języki publikacji: EN

Abstrakty

EN

We deal with unconditional convergence of series and some special classes of subsets of N.

Słowa kluczowe

EN

l-group; ideal; ideal order and (D)-convergence; limit theorem; matrix theorem; Schur theorem; unconditional convergence

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2010
• Tom: Vol. 50, [Z] 2
• Strony: 161--174
• Opis fizyczny: Bibliogr.

Twórcy

autor

Boccuto A.

autor

Dimitriou X.

autor

Papanastassiou N.

• Department of Mathematics and Computer Sciences, University of Perugia via Vanvitelli 1, I-06123 Perugia, Italy,

Bibliografia

• [1] A. Aizpuru and M. Nicasio-Llach, About the statistical uniform convergence, Bull. Braz. Math. Soc. 39 (2008), 173-182.
• [2] A. Aizpuru, M. Nicasio-Llach and F. Rambla-Barreno, A Remark about the Orlicz-Pettis Theorem and the Statistical Convergence, Acta Math. Sinica, English Ser. 26 (2) (2010), 305-31.
• [3] P. Antosik and C. Swartz, Matrix methods in Analysis, Lecture Notes in Mathematics 1113 Springer-Verlag, 1985.
• [4] S. J. Bernau, Unique representation of Archimedean lattice group and normal Archimedean lattice rings, Proc. Lond. Math. Soc. 15 (1965), 599-631.
• [5] A. Boccuto, Egorov property and weak _-distributivity in l-groups, Acta Math. (Nitra) 6 (2003), 61-66.
• [6] A. Boccuto, X. Dimitriou and N. Papanastassiou, Basic matrix theorems for I-convergence in (l)-groups, Technical Report 2010/6, Mathematical Department, University of Perugia, submitted.
• [7] A. Boccuto, X. Dimitriou and N. Papanastassiou, Countably additive restrictions and limit theorems in (l)-groups, Atti Sem. Mat. Fis. Univ. Modena e Reggio Emilia (2010), to appear.
• [8] A. Boccuto and N. Papanastassiou, Schur and Nikod´ym convergence-type theorems in Riesz spaces with respect to the (r)-convergence, Atti Sem. Mat. Fis. Univ. Modena e Reggio Emilia 55 (2007), 33-46.
• [9] A. Boccuto, B. Riečan and M. Vrábelová, Kurzweil-Henstock Integral in Riesz Spaces, Bentham Science Publ., e-book, 2009.
• [10] A. Boccuto and V. A. Skvortsov, Some applications of the Maeda-Ogasawara-Vulikh representation theorem to Differential Calculus in Riesz spaces, Acta Math. (Nitra) 9 (2006), 13-24; Addendum to: Some applications of the Maeda-Ogasawara-Vulikh representation theorem to Differential Calculus in Riesz spaces", ibidem 12 (2009), 39-46.
• [11] R. Demarr, Order convergence and topological convergence, Proc. Amer. Math. Soc. 16 (4) (1965), 588-590.
• [12] P. Kostyrko, T. šalát and W. Wilczynski, I-convergence, Real Anal. Exch. 26 (2000/2001), 669-685.
• [13] R. May and C. McArthur, Comparison of two types of order convergence with topological convergence in an ordered topological vector space, Proc. Amer. Math. Soc. 63 (1) (1977), 49-55.
• [14] B. Riečan and T. Neubrunn, Integral, Measure and Ordering, Kluwer Academic Publishers/Ister Science, Dordercht/Bratislava, 1997.
• [15] B. Riečan and P. Volauf, On a technical lemma in lattice ordered groups, Acta Math. Univ. Comenian. 44/45 (1984), 31-36.