Hostname: page-component-84b7d79bbc-c654p Total loading time: 0 Render date: 2024-07-25T07:56:41.075Z Has data issue: false hasContentIssue false
  • English
  • Français

Smoothness and the asymptotic-norming properties of Banach spaces

Published online by Cambridge University Press:  17 April 2009

Zhibao Hu  and
Bor-Luh Lin
Zhibao Hu
Affiliation:
Department of MathematicsUniversity of IowaIowa City IA 52242United States of America
Bor-Luh Lin
Affiliation:
Department of MathematicsUniversity of IowaIowa City IA 52242United States of America
Rights & Permissions [Opens in a new window]

Abstract

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.

We study some smoothness properties of a Banach space X that are related to the weak* asymptotic-norming properties of the dual space X*. These properties imply that X is an Asplund space and are related to the duality mapping of X.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 2 , April 1992 , pp. 285 - 296
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Giles, J.R., Gregory, D.A. and Sims, B., ‘Geometrical implications of upper semi-continuity of the duality mapping on a Banach space’, Pacific J. Math. 79 (1978), 99–105.CrossRefGoogle Scholar
[2]Godefroy, G., ‘Nicely smooth Banach spaces’, in Longhorn Notes, pp. 117–124 (The University of Texas at Austin, 1984–1985).Google Scholar
[3]Godefroy, G., ‘Boundaries of a convex set and interpolation sets’, Math. Ann. 277 (1987), 173–184.CrossRefGoogle Scholar
[4]Godefroy, G. and Kalton, N., ‘The ball topology and its applications’, Contemporary Math. 85 (1989), 195–237.CrossRefGoogle Scholar
[5]Godefroy, G. and Saphar, P.D., ‘Duality in spaces of operators and smooth norms on Banach spaces’, Illinois J. Math. 32 (1988), 672–695.CrossRefGoogle Scholar
[6]Haydon, R., ‘A counterexample to several questions about scattered compact spaces’, Bull. London Math. Soc. 22 (1990), 261–268.CrossRefGoogle Scholar
[7]Haydon, R., ‘An extreme point criterion for separability of a dual Banach space and a new proof of a theorem of Carson’, Quarter J. Math. 27 (1976), 379–385.Google Scholar
[8]Hu, Zbibao and Lin, Bor-Luh, ‘On the asymptotic-norming property of Banach spaces’, in Proc. Conference on Function Spaces, SIUE: Lecture Notes in Pure and Applied Math. (Marcel-Dekker, to appear).Google Scholar
[9]James, R.C. and Ho, A., ‘The asymptotic-norming and Radon-Nikodym properties for Banach spaces’, Ark. Mat. 19 (1981), 53–70.CrossRefGoogle Scholar
[10]Smith, M. and Sullivan, F., Extremely smooth Banach spaces: Lecture Notes in Math. 604 (Springer-Verlag, Berlin, Heidelberg, New York, 1977).Google Scholar
[11]Sullivan, F., ‘Geometrical properties determined by the higher duals of a Banach space’, Illinois J. Math. 21 (1977), 315–331.CrossRefGoogle Scholar
[12]Talagrand, M., ‘Renormage de quelques C(K)’, Israel J. Math. 54 (1986), 327–324.CrossRefGoogle Scholar
[13]Zhang, Wenyao, ‘A new smoothness of Banach spaces’, in Proc. Analysis Conference, Singapore 1986, pp. 301–304 (Elsevier Science Publishers, North Holland, 1988).CrossRefGoogle Scholar
[14]Zippin, M., ‘A remark on basis and reflexivity in Banach spaces’, Israel J. Math. 6 (1968), 74–79.CrossRefGoogle Scholar