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2014 | 12 | 7 | 1026-1039
Tytuł artykułu

Rich families and elementary submodels

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We compare two methods of proving separable reduction theorems in functional analysis - the method of rich families and the method of elementary submodels. We show that any result proved using rich families holds also when formulated with elementary submodels and the converse is true in spaces with fundamental minimal system and in spaces of density ℵ1. We do not know whether the converse is true in general. We apply our results to show that a projectional skeleton may be without loss of generality indexed by ranges of its projections.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
7
Strony
1026-1039
Opis fizyczny
Daty
wydano
2014-07-01
online
2014-04-03
Twórcy
autor
Bibliografia
  • [1] Borwein J.M., Moors W.B., Separable determination of integrability and minimality of the Clarke subdifferential mapping, Proc. Amer. Math. Soc., 2000, 128(1), 215–221 http://dx.doi.org/10.1090/S0002-9939-99-05001-7
  • [2] Cúth M., Separable reduction theorems by the method of elementary submodels, Fund. Math., 2012, 219(3), 191–222 http://dx.doi.org/10.4064/fm219-3-1
  • [3] Cúth M., Noncommutative Valdivia compacta, Comment. Math. Univ. Carolin., 2014, 55(1), 53–72
  • [4] Cúth M., Simultaneous projectional skeletons, J. Math. Anal. Appl., 2014, 411(1), 19–29 http://dx.doi.org/10.1016/j.jmaa.2013.09.020
  • [5] Cúth M., Rmoutil M., σ-porosity is separably determined, Czechoslovak Math. J., 2013, 63(1), 219–234 http://dx.doi.org/10.1007/s10587-013-0015-3
  • [6] Cúth M., Rmoutil M., Zelený M., On separable determination of σ-P-porous sets in Banach spaces, preprint avaiable at http://arxiv.org/abs/1309.2174
  • [7] Fabian M., Ioffe A., Separable reduction in the theory of Fréchet subdifferentials, Set-Valued Var. Anal., 2013, 21(4), 661–671 http://dx.doi.org/10.1007/s11228-013-0256-1
  • [8] Ferrer J., Koszmider P., Kubiś W., Almost disjoint families of countable sets and separable complementation properties, J. Math. Anal. Appl., 2013, 401(2), 939–949 http://dx.doi.org/10.1016/j.jmaa.2013.01.008
  • [9] Garbulińska J., Kubiś W., Remarks on Gurariĭ spaces, Extracta Math., 2011, 26(2), 235–269
  • [10] Hájek P., Montesinos Santalucía V., Vanderwerff J., Zizler V., Biorthogonal Systems in Banach Spaces, CMS Books Math./Ouvrages Math. SMC, 26, Springer, New York, 2008
  • [11] Ioffe A.D., On the theory of subdifferentials, Adv. Nonlinear Anal., 2012, 1(1), 47–120
  • [12] Kąkol J., Kubiś W., López-Pellicer M., Descriptive Topology in Selected Topics of Functional Analysis, Dev. Math., 24, Springer, New York, 2011 http://dx.doi.org/10.1007/978-1-4614-0529-0
  • [13] Kalenda O.F.K., Kubiś W., Complementation in spaces of continuous functions on compact lines, J. Math. Anal. Appl., 2012, 386(1), 241–257 http://dx.doi.org/10.1016/j.jmaa.2011.07.057
  • [14] Kubiś W., Banach spaces with projectional skeletons, J. Math. Anal. Appl., 2009, 350(2), 758–776 http://dx.doi.org/10.1016/j.jmaa.2008.07.006
  • [15] Kubiś W., Michalewski H., Small Valdivia compact spaces, Topology Appl., 2006, 153(14), 2560–2573 http://dx.doi.org/10.1016/j.topol.2005.09.010
  • [16] Kunen K., Set Theory, Stud. Logic Found. Math., 102, North-Holland, Amsterdam, 1980
  • [17] Lin P., Moors W.B., Rich families, W-spaces and the product of Baire spaces, Math. Balkanica (N.S.), 2008, 22(1–2), 175–187
  • [18] Lindenstrauss J., Preiss D., Tišer J., Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces, Ann. of Math. Stud., 179, Princeton University Press, Princeton, 2012
  • [19] Moors W.B., Spurný J., On the topology of pointwise convergence on the boundaries of L 1-preduals, Proc. Amer. Math. Soc., 2009, 137(4), 1421–1429 http://dx.doi.org/10.1090/S0002-9939-08-09708-6
  • [20] Todorcevic S., Biorthogonal systems and quotient spaces via Baire category methods, Math. Ann., 2006, 335(3), 687–715 http://dx.doi.org/10.1007/s00208-006-0762-7
  • [21] Zajíček L., Generic Fréchet differentiability on Asplund spaces via a.e. strict differentiability on many lines, J. Convex Anal., 2012, 19(1), 23–48
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0400-z
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