Hostname: page-component-84b7d79bbc-x5cpj Total loading time: 0 Render date: 2024-07-27T21:45:50.269Z Has data issue: false hasContentIssue false
  • English
  • Français

The day norm and Gruenhage compacta

Published online by Cambridge University Press:  17 April 2009

M. Fabian ,
V. Montesinos  and
V. Zizler
M. Fabian
Affiliation:
Mathematical Institute of the Czech Academy of Sciences, Žitná 25, 11567, Prague 1, Czech Republic, e-mail: fabian@math.cas.cz
V. Montesinos
Affiliation:
Department of Mathematical Sciences, University of Alberta, 632 Central Academic Building, Edmonton, Alberta T6G 2G1, Canada, e-mail: vzizler@math.ualberta.ca
V. Zizler
Affiliation:
Departamento de Matemática Aplicada, E.T.S.I. Telecomunicación, Universidad Politécnica de Valencia, C/Vera, s/n. 46071 Valencia, Spain, e-mail: vmontesinos@mat.upv.es
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A close connection between the strict convexity of the Day norm to the concept of the Gruenhage compacta is shown. As a byproduct we give an elementary characterisation of Gul'ko compacta in the sigma-product of lines and a more elementary proof of Mercourakis' renorming result for Vašák spaces.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 3 , June 2004 , pp. 451 - 456
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Argyros, S. and Mercourakis, S., ‘On weakly Lindelöf Banach spaces’, Rocky Mountain J. Math. 23 (1993), 395–446.Google Scholar
[2]Deville, R., Godefroy, G. and Zizler, V., Smoothness and renormings in Banach spaces, Pitman Monographs 64 (Longman Scientific and Technical, Harlow, 1993).Google Scholar
[3]Fabian, M., Gâteaux differentiability of convex functions and topology. Weak Asplund Spaces (John Wiley & Sons, New York, 1997).Google Scholar
[4]Fabian, M., Habala, P., Hájek, P., Pelant, J., Montesinos, V. and Zizler, V., Functional analysis and infinite dimensional geometry, CMS Books in Mathematics 8 (Springer-Verlag, New York, 2001).Google Scholar
[5]Fabian, M., Godefroy, G., Hájek, P. and Zizler, V., ‘Hilbert-generated spaces’, J. Functional Analysis 200 (2003), 301–323.Google Scholar
[6]Fabian, M., Godefroy, G., Montesinos, V. and Zizler, V., ‘WCG spaces and their relatives’ (to appear).Google Scholar
[7]Fabian, M., Montesinos, V. and Zizler, V., ‘Biorthogonal systems in weakly Lindelöf spaces’, Canad. Math. Bull. (to appear).Google Scholar
[8]Farmaki, V., ‘The structure of Eberlein, uniformly Eberlein and Talagrand compact spaces in Σ(IRΓ)’, Fund. Math. 128 (1987), 15–28.CrossRefGoogle Scholar
[9]Gruenhage, G., ‘A note on Gul'ko compact spaces’, Proc. Amer. Math. Soc. 100 (1987), 371–376.Google Scholar
[10]Mercourakis, S., ‘On weakly countably determined Banach spaces’, Trans. Amer. Math. Soc. 300 (1987), 307–327.Google Scholar
[11]Raja, M., ‘Weak* locally uniformly rotund norms and desriptive compact spaces’, J. Functional Anal. 197 (2003), 1–13.Google Scholar
[12]Ribarska, N.K., ‘Internal characterization of fragmentable spaces’, Mathematica 34 (1987), 243–257.Google Scholar
[13]Sokolov, G.A., ‘On some classes of compact spaces lying in Σ-products’, Comment. Math. Univ. Carolin. 25 (1984), 219–231.Google Scholar
[14]Tacon, D.G., ‘The conjugate of a smooth Banach space’, Bull. Austral. Math. Soc. 2 (1970), 415–425.Google Scholar