Author:
Carothers N. L.,Dilworth S. J.,Trautman D. A.
Abstract
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.
Publisher
Cambridge University Press (CUP)
Reference6 articles.
1. Positive bases in Banach spaces;Davis;Rev. Roumaine Math. Pures Appl.,1971
2. Isometries on Lp,1;Carothers;Trans. Amer. Math. Soc.,1986
3. Classical Banach Spaces II
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