Hostname: page-component-669899f699-rg895 Total loading time: 0 Render date: 2025-04-26T22:27:15.639Z Has data issue: false hasContentIssue false
  • English
  • Français

Uniform Kadec–Klee–Huff properties of vector-valued Hardy spaces

Published online by Cambridge University Press:  24 October 2008

P. N. Dowling  and
C. J. Lennard
P. N. Dowling
Affiliation:
Miami University, Oxford, Ohio 4506, USA
C. J. Lennard
Affiliation:
University of Pittsburgh, Pittsburgh, PA 15260, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

In [8] Partington showed that a Banach space X is uniformly convex if and only if Lp([0, 1], X) has the uniform Kadec–Klee–Huff property with respect to the weak topology (UKKH (weak)), where 1 < p < ∞. In this note we will characterize the Banach spaces X such that HP(D, X) has UKKH (weak), where 1 ≤ p < ∞. Similar results for UKKH (weak*) are also obtained. These results (and proofs) are quite different from Partington's result (and proof).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 114 , Issue 1 , July 1993 , pp. 25 - 30
Copyright
Copyright © Cambridge Philosophical Society 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1]Besbes, M., Dilworth, S., Dowling, P. and Lennard, C.. New convexity and fixed point properties in Hardy and Lebesgue–Bochner spaces. J. Fund. Anal., to appear.Google Scholar
[2]Dowling, P. N.. Duality in some vector-valued function spaces. Rocky Mountain J. Math. 22 (1992), 511–518.CrossRefGoogle Scholar
[3]Dowling, P. N. and Lennard, C. J.. On uniformly H-convex complex quasi-Banach spaces. Bull. Sci. Math., to appear.Google Scholar
[4]Van Dulst, D. and Sims, B.. Fixed points of non-expansive mappings and Chebyshev centers in Banach spaces with norms of type (KK). Banach Space Theory and its Applications, Proc. Bucharest 1981, Lecture Notes in Math. 991 (Springer-Verlag, 1983), 34–43.Google Scholar
[5]Huff, R. E.. Banach spaces which are nearly uniformly convex. Rocky Mountain J. of Math. 10 (1980), 743–749.CrossRefGoogle Scholar
[6]Kirk, W. A.. A fixed point theorem for mappings which do not increase distances. Amer. Math. Monthly 72 (1965), 1004–1006.CrossRefGoogle Scholar
[7]Lennard, C. J.. On the Schur and Kadec–Klee properties in Banach spaces, preprint.Google Scholar
[8]Partington, J. R.. On nearly uniformly convex Banach spaces. Math. Proc. Camb. Phil. Soc. 93 (1983), 127–129.CrossRefGoogle Scholar
[9]Xu, Q.. Inègalités pour les martingales de Hardy et renormage des espaces quasi-normés. C.R. Acad. Sci. Paris 306, série I (1988), 601–604.Google Scholar
[10]Xu, Q.. Convexités uniformes et inégalités de martingales. Math. Ann. 287 (1990), 193–211.Google Scholar