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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-article-BUS8-0012-0007

Czasopismo

Commentationes Mathematicae

Tytuł artykułu

Unconditional convergence in lattice groups with respect to ideals

Autorzy Boccuto, A.  Dimitriou, X.  Papanastassiou, N. 
Treść / Zawartość http://wydawnictwa.ptm.org.pl/index.php/commentationes-mathematicae/ http://www.staff.amu.edu.pl/~commath/
Warianty tytułu
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, boccuto@yahoo.it
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.
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