Functiones et Approximatio Commentarii Mathematici

WCG spaces and their subspaces grasped by projectional skeletons

Marián Fabian and Vicente Montesinos

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Weakly compactly generated Banach spaces and their subspaces are characterized by the presence of projectional skeletons with some additional properties. We work with real spaces. However the presented statements can be extended, without much extra effort, to complex spaces.

Article information

Funct. Approx. Comment. Math., Volume 59, Number 2 (2018), 231-250.

First available in Project Euclid: 26 October 2018

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10] 46B20: Geometry and structure of normed linear spaces

Banach space weakly compactly generated space, weakly Lindelöf determined space rich family commutative projectional skeleton projectional resolution of the identity


Fabian, Marián; Montesinos, Vicente. WCG spaces and their subspaces grasped by projectional skeletons. Funct. Approx. Comment. Math. 59 (2018), no. 2, 231--250. doi:10.7169/facm/1721.

Export citation


  • D. Amir and J. Lindenstrauss, The structure of weakly compact sets in Banach spaces, Annals of Math. 88 (1968), 35–46.
  • J.,M. Borwein and W.,B. Moors, Separable determination of integrability and minimality of the Clarke subdifferential mapping, Proc. Amer. Math. Soc. 128 (2000), 215–221.
  • M. Cúth, Private communication.
  • M. Cúth, M. Fabian, Rich families and projectional skeletons in Asplund WCG spaces, J. Math. Anal. Appl. 448 (2017), 1618–1632.
  • J. Diestel, Geometry of Banach spaces –- Selected topics, Lect. Notes in Math., Springer-Verlag, Berlin 1975.
  • M.,J. Fabian, Gâteaux differentiability of convex functions and topology, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, Inc., New York, 1997. Weak Asplund spaces, A Wiley-Interscience Publication.
  • M. Fabian, G. Godefroy, V. Montesinos, and V. Zizler, Inner characterizations of WCG spaces and their relatives, J. Math. Analysis Appl. 297 (2004), 419–455.
  • M. Fabian, P. Habala, P. Hájek, V. Montesinos, and V. Zizler, Banach space theory. The basis for linear and nonlinear analysis., CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Springer, New York, 2011.
  • V. Farmaki, The structure of Eberlein and Talagrand comnpact spaces in $\Sigma(\R^\Gamma)$, Fund. Math. 128 (1987), 15–28.
  • P. Hájek, V. Montesinos, J. Vanderwerff, and V. Zizler, Biorthogonal systems in Banach spaces, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 26, Springer, New York, 2008.
  • W. Kubiś, Banach spaces with projectional skeletons, J. Math. Anal. Appl. 350 (2009), 758–776.
  • W. Kubiś, H. Michalewski, Small Valdivia compact spaces, Topology Appl. 153 (2006), no. 14, 2560–2573.
  • J. Kąkol, W. Kubiś, and M. López-Pellicer, Descriptive topology in selected topics of functional analysis, Vol. 24 of Developments in Mathematics, Springer, New York, 2011.
  • O.,F.,K. Kalenda, Complex Banach spaces with Valdivia dual unit ball, Extracta Math. 20 (2005), 243–259.
  • M. Valdivia, Resolution of the identity in certain Banach spaces, Collect. Math. 39 (1988), 17–140.