If you need an accessible version of this item please contact JSTOR User Support

Differentiable Functions and Rough Norms on Banach Spaces

E. B. Leach and J. H. M. Whitfield
Proceedings of the American Mathematical Society
Vol. 33, No. 1 (May, 1972), pp. 120-126
DOI: 10.2307/2038183
Stable URL: http://www.jstor.org/stable/2038183
Page Count: 7
  • Download PDF
  • Cite this Item

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support
Differentiable Functions and Rough Norms on Banach Spaces
Preview not available

Abstract

The main result is that if $X$ is a real Banach space, such that the density character of $X^\ast$ is greater than that of $X$, then there does not exist any real-valued Fréchet differentiable function on $X$ with bounded nonempty support.

Page Thumbnails

  • Thumbnail: Page 
120
    120
  • Thumbnail: Page 
121
    121
  • Thumbnail: Page 
122
    122
  • Thumbnail: Page 
123
    123
  • Thumbnail: Page 
124
    124
  • Thumbnail: Page 
125
    125
  • Thumbnail: Page 
126
    126