Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-18T05:29:13.105Z Has data issue: false hasContentIssue false
  • English
  • Français

A subdifferential characterisation of Banach spaces with the Radon–Nikodym property

Published online by Cambridge University Press:  17 April 2009

J. R. Giles
J. R. Giles
Affiliation:
Department of Mathematics, The University of Newcastle, New South Wales 2308, Australia
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 Banach space has the Radon–Nikodym Property if and only if every continuous weak* lower semi–continuous gauge on the dual space has a point of its domain where its subdifferential is contained in the natural embedding.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 66 , Issue 2 , October 2002 , pp. 313 - 316
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Bachir, M. and Daniilidis, A., ‘A dual characterisation of the Radon–Nikodym Property’, Bull. Austral. Math. Soc. 62 (2000), 379–387.Google Scholar
[2]Bourgin, R., Geometric aspects of convex sets with the Radon–Nikodym Property, Lecture notes in Mathematics, 993 (Springer-Verlag, Berlin, Heidelberg, New York, 1983).Google Scholar
[3]Collier, J., ‘The dual of a space with the Randon–Nikodym Property’, Pacific J. Math. 64 (1976), 103–106.CrossRefGoogle Scholar
[4]Giles, J.R., ‘Comparable differentiability characterisations of two classes of Banach spaces’, Bull. Austral. Math. Soc. 56 (1997), 263–272.Google Scholar
[5]Giles, J.R., ‘Comparable characterisations of two classes of Banach spaces by subdifferentials’, Bull. Austral. Math. Soc. 58 (1998), 155–158.CrossRefGoogle Scholar
[6]Godefroy, G., ‘Metric characterisarions of first Baire class linear forms and octahedral norms’, Studia Math. 95 (1989), 1–15.Google Scholar
[7]Phelps, R.R., Convex functions, monotone operators and differentiability (2nd edition), Lecture notes in Mathematics 1364, (Springer Verlag, Berlin, Heidelberg, New York, 1993).Google Scholar
[8]Phelps, R.R., ‘Weak* support points of convex sets in E *’, Israel J. Math. 2 (1964), 177–182.Google Scholar