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2015 | 13 | 1 |
Tytuł artykułu

Extremal properties of the set of vector-valued Banach limits

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this manuscript we find another class of real Banach spaces which admit vector-valued Banach limits different from the classes found in [6, 7]. We also characterize the separating subsets of ℓ∞(X). For this we first need to study when the space of almost convergent sequences is closed in the space of bounded sequences, which turns out to happen only when the underlying space is complete. Finally, a study on the extremal structure of the set of vector-valued Banach limits is conducted when the underlying normed space is a Hilbert space.We also reach the conclusion that the set of vector-valued Banach limits is not a convex component of BCL(ℓ∞(X),X), provided that X is a 1-injective Banach space satisfying that the underlying compact Hausdorff topological space has isolated points.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2015-06-23
zaakceptowano
2015-10-16
online
2015-11-03
Twórcy
  • Department of Mathematics, University of Cadiz, Puerto Real 11510, Spain
Bibliografia
  • [1] Banach, S., Théorie des opérations linéaires, Chelsea Publishing company, New York, 1978
  • [2] Ahmad, Z.U., Mursaleen, M., An application of Banach limits, Proc. Amer. Math. Soc., 1988, 103, 244-246
  • [3] Semenov, E., Sukochev, F., Extreme points of the set of Banach limits, Positivity, 2013, 17, 163-170[WoS]
  • [4] Semenov, E., Sukochev, F., Invariant Banach limits and applications, J. Funct. Anal., 2010, 259, 1517-1541[WoS]
  • [5] Semenov, E., Sukochev, F., Usachev, A., Structural properties of the set of Banach limits, Dokl. Math., 2011, 84, 802-803[WoS]
  • [6] Armario, R., García-Pacheco, F.J., Pérez-Fernández, F.J., On Vector-Valued Banach Limits, Funct. Anal. Appl., 2013, 47, 315-318[WoS]
  • [7] Armario, R. García-Pacheco, F.J., Pérez-Fernández, F.J., Fundamental Aspects of Vector-Valued Banach Limits, Izv. Math., 2016,80, (in press)
  • [8] Rosenthal, H., On injective Banach spaces and the spaces C .S/, Bull. Amer. Math. Soc., 1969, 75, 824-828
  • [9] Wolfe, J., Injective Banach spaces of continuous functions, Trans. Amer. Math. Soc., 1978, 235, 115-139
  • [10] Lorentz, G., A contribution to the theory of divergent sequences, Acta Math., 1948, 80, 167-190
  • [11] Boos, J., Classical and Modern Methods in summability, Oxford University Press, 2000
  • [12] Mursaleen, M., On some new invariant matrix methods of summability, Quart. Jour. Math. Oxford, 1983, 34, 77-86
  • [13] Mursaleen, M., On A-invariant mean and A-almost convergence, Analysis Mathematica, 2011, 37, 173-180[WoS]
  • [14] Mursaleen, M., Applied Summability Methods, Springer Briefs, Heidelberg New York Dordrecht London, 2014
  • [15] Raimi, R.A., Invariant means and invariant matrix methods of summability, Duke Math. J., 1963, 30, 81-94
  • [16] Aizpuru, A., Armario, R., García-Pacheco, F.J., Pérez-Fernández, F.J., Banach limits and uniform almost summability, J. Math.Anal. Appl., 2011, 379, 82-90
  • [17] Aizpuru, A., Armario, R., García-Pacheco, F.J., Pérez-Fernández, F.J., Vector-Valued Almost Convergence and ClassicalProperties in Normed Spaces, Proc. Indian Acad. Sci. Math., 2014, 124, 93-108[WoS]
  • [18] García-Pacheco, F.J., Convex components and multi-slices in topological vector spaces, Ann. Funct. Anal., 2015, 6, 73-86[WoS]
  • [19] Day, M.M., Normed linear spaces, 3rd edition, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 21, Springer-Verlag,New York-Heidelberg, 1973
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0067
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