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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

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