Skip to main content Accessibility help
×
Home

The day norm and Gruenhage compacta

  • M. Fabian (a1), V. Montesinos (a2) and V. Zizler (a3)

Extract

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.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      The day norm and Gruenhage compacta
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      The day norm and Gruenhage compacta
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      The day norm and Gruenhage compacta
      Available formats
      ×

Copyright

References

Hide All
[1]Argyros, S. and Mercourakis, S., ‘On weakly Lindelöf Banach spaces’, Rocky Mountain J. Math. 23 (1993), 395446.
[2]Deville, R., Godefroy, G. and Zizler, V., Smoothness and renormings in Banach spaces, Pitman Monographs 64 (Longman Scientific and Technical, Harlow, 1993).
[3]Fabian, M., Gâteaux differentiability of convex functions and topology. Weak Asplund Spaces (John Wiley & Sons, New York, 1997).
[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).
[5]Fabian, M., Godefroy, G., Hájek, P. and Zizler, V., ‘Hilbert-generated spaces’, J. Functional Analysis 200 (2003), 301323.
[6]Fabian, M., Godefroy, G., Montesinos, V. and Zizler, V., ‘WCG spaces and their relatives’ (to appear).
[7]Fabian, M., Montesinos, V. and Zizler, V., ‘Biorthogonal systems in weakly Lindelöf spaces’, Canad. Math. Bull. (to appear).
[8]Farmaki, V., ‘The structure of Eberlein, uniformly Eberlein and Talagrand compact spaces in Σ(IRΓ)’, Fund. Math. 128 (1987), 1528.
[9]Gruenhage, G., ‘A note on Gul'ko compact spaces’, Proc. Amer. Math. Soc. 100 (1987), 371376.
[10]Mercourakis, S., ‘On weakly countably determined Banach spaces’, Trans. Amer. Math. Soc. 300 (1987), 307327.
[11]Raja, M., ‘Weak* locally uniformly rotund norms and desriptive compact spaces’, J. Functional Anal. 197 (2003), 113.
[12]Ribarska, N.K., ‘Internal characterization of fragmentable spaces’, Mathematica 34 (1987), 243257.
[13]Sokolov, G.A., ‘On some classes of compact spaces lying in Σ-products’, Comment. Math. Univ. Carolin. 25 (1984), 219231.
[14]Tacon, D.G., ‘The conjugate of a smooth Banach space’, Bull. Austral. Math. Soc. 2 (1970), 415425.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Related content

Powered by UNSILO

The day norm and Gruenhage compacta

  • M. Fabian (a1), V. Montesinos (a2) and V. Zizler (a3)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.