Properties of the Holmes space |
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| Authors: | VP Fonf P Wojtaszczyk |
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| Institution: | a Department of Mathematics, Ben-Gurion University of the Negev, PO Box 653, Beer-Sheva 84105, Israel
b Institut of Applied Mathematics, University of Warsaw, 02-097 Warszawa, ul. Banacha 2, Poland |
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| Abstract: | The following properties of the Holmes space H are established:- (i)
- H has the Metric Approximation Property (MAP).
- (ii)
- The w∗-closure of the set of extreme points of the unit ball BH∗ of the dual space H∗ is the whole ball BH∗.
A family of compact subsets X⊂U of the Urysohn space is described such that the Lipschitz-free space F(X) has a finite-dimensional decomposition and is not complemented in H. |
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| Keywords: | primary 46B20 secondary 54E50 |
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