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On the geometry of the unit spheres of the Lorentz spaces Lw,1

Published online by Cambridge University Press:  18 May 2009

N. L. Carothers ,
S. J. Dilworth  and
D. A. Trautman
N. L. Carothers
Affiliation:
Bowling Green State University, Bowling Green, Ohio 43403, U.S.A.
S. J. Dilworth
Affiliation:
University of South Carolina, Columbia, South Carolina 29208, U.S.A.
D. A. Trautman
Affiliation:
The Citadel, Charleston, South Carolina 29409, U.S.A.
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We identify the extreme points of the unit sphere of the Lorentz space Lw,1 This yields a characterization of the surjective isometries of Lw,1(0,1). Our main result is that every element in the unit sphere of Lw,1 is the barycenter of a unique Borel probability measure supported on the extreme points of the unit sphere of Lw,1.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 1 , January 1992 , pp. 21 - 25
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

REFERENCES

1.Bennett, C. and Sharpley, R. C., Interpolation of Operators (Academic Press, 1988).Google Scholar
2.Carothers, N. L. and Turett, B., Isometries on L p,1, Trans. Amer. Math. Soc. 297 (1986), 95–103.Google Scholar
3.Davis, W. J., Positive bases in Banach spaces, Rev. Roumaine Math. Pures Appl. 16 (1971), 487–492.Google Scholar
4.Hewitt, E. and Stromberg, K., Real and Abstract Analysis. (Springer-Verlag, 1975).Google Scholar
5.Lindenstrauss, J. and Tzafriri, L., Classical Banach Spaces II: Function Spaces, Ergebnisse Math. 2. Folge 97 (Springer-Verlag, 1979).CrossRefGoogle Scholar
6.Royden, H. L., Real Analysis, 3rd. Ed. (Macmillan, 1988).Google Scholar