Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-27T14:37:12.566Z Has data issue: false hasContentIssue false
  • English
  • Français

The λ-property in schreier's space S and the Lorentz space d(a, 1)

Published online by Cambridge University Press:  18 May 2009

Thaddeus J. Shura  and
David Trautman
Thaddeus J. Shura
Affiliation:
Kent State Universityat SalemSalem, Ohio 44460, U.S.A.
David Trautman
Affiliation:
The CitadelCharlestonSouth Carolina 29409, U.S.A.
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 add Schreier's space S and the Lorentz space d(a, 1) to the list of classical Banach spaces which enjoy the λ-property, investigate the extreme point structure of S, and show that d(a, 1) has a λ-function which is continuous on Sd(a, 1), though not even uniformly so.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 3 , September 1990 , pp. 277 - 284
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

REFERENCES

1.Aron, R. M. and Lohman, R. H., A geometric function determined by extreme points of the unit ball of a normed space, Pacific J. Math. 127 (1987), 209–236.CrossRefGoogle Scholar
2.Casazza, P. G. and Shura, T. J., Tsirelson's space, Lecture Notes in Mathematics No 1363 (Springer-Verlag, 1989).CrossRefGoogle Scholar
3.Granero, A. S., On the Aron–Lohman's λ-property (preprint).Google Scholar
4.Granero, A. S., The λ-function in the spaces (⊕ Σ X)p and L p(μ, X) (preprint).Google Scholar
5.Halmos, P. R., A Hilbert space problem book, (Van Nostrand, 1967).Google Scholar
6.Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces II; function spaces (Springer-Verlag, 1979).CrossRefGoogle Scholar
7.Lohman, R. H., The λ-property in Banach spaces, in Banach Space Theory, Contemporary Mathematics 85 (1989), 345–354.CrossRefGoogle Scholar
8.Lohman, R. H., Shura, T. J., Calculation of the λ-function for several classes of normed linear spaces, in Nonlinear and convex analysis: Proceedings in honor of Ky Fan (Marcel Dekker, 1987).Google Scholar
9.Shura, T. J., Dissertation, Kent State University, (to appear).Google Scholar
10.Davis, W. J., Positive bases in Banach spaces, Rev. Roumaine Math. Pures Appl., 16 (1971), 487–492.Google Scholar