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On the entropy of the convex hull of finite sets
Author(s):
Ioanna
Kyrezi
Journal:
Proc. Amer. Math. Soc.
128
(2000),
2393-2403.
MSC (2000):
Primary 46B07, 46B20, 47B37, 52A38
Posted:
November 29, 1999
MathSciNet review:
1662261
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Abstract:
We give estimates for the entropy numbers and the Gel fand diameters of the symmetric convex hull of a finite number of points in a Banach or a Hilbert space.
References:
- [BM]
- J. Bourgain and V. D. Milman, New volume ratio properties for convex symmetric bodies in
 , Invent. Math. 88 (1987), 319-340. MR 88f:52013 - [BP]
- K. Ball and A. Pajor, The entropy of convex bodies with ``few'' extreme points, London Math. Soc. Lecture Notes Series 158 (1990), 25-32. MR 93b:46024
- [BP2]
- -, Convex bodies with few faces, Proc. Amer. Math. Soc. 110 (1990), 225-231. MR 90m:52011
- [C]
- B. Carl, Inequalities of Bernstein-Jackson type and the degree of compactness of operators in Banach spaces, Ann. Inst. Fourier 35 (3) (1985), 79-118. MR 86m:47022
- [CP]
- B. Carl and A. Pajor, Gel
 fand numbers of operators with values in Hilbert spaces, Invent. Math. 94 (1988), 479-504. MR 90d:46023 - [CKP]
- B. Carl, I. Kyrezi and A. Pajor, Metric entropy of convex hulls in Banach spaces, to appear in the Journal of London Mathematical Society.
- [CS]
- B. Carl and I. Stephani, Entropy, compactness and the approximation of operators, Cambridge University Press (1990). MR 92e:47002
- [LT]
- J. Lindenstrauss and C. Tzafriri, Classical Banach spaces, vol. 1,2, Springer Verlag (1977/79). MR 58:17766; MR 81c:46001
- [Pie]
- A. Pietsch Operator ideals, Berlin (1978), North Holland (1980). MR 81j:47001
- [P1]
- G. Pisier, Volume inequalities in the geometry of Banach spaces, Cambridge University Press (1989).
- [P2]
- -, Remarques sur un résultat non publié de B. Maurey, Séminaire d'Analyse Fonctionnelle, Ecole Polytechnique-Palaiseau, Exposé 5 (1980/1981). MR 83h:46026
- [S]
- L. Santaló, Un invariante afin para los cuerpos convexos den espacio de
 dimensiones, Portugal Math. 8 (1949), 155-161.
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Additional Information:
Ioanna
Kyrezi
Affiliation:
Université de Marne-la-Vallée, Equipe d'Analyse et de Mathématiques Appliquées, Cité Descartes, 5 Bd Descartes, Champs sur Marne, 77454 Marne-la-Vallée Cedex 2, France
Email:
kyrezi@math.univ-mlv.fr
DOI:
10.1090/S0002-9939-99-05302-2
PII:
S 0002-9939(99)05302-2
Keywords:
Metric entropy,
entropy numbers,
Gel$'$fand numbers
Received by editor(s):
June 14, 1998
Received by editor(s) in revised form:
September 22, 1998
Posted:
November 29, 1999
Additional Notes:
The author's research was supported by Hellenic S.S.F
Communicated by:
Dale Alspach
Copyright of article:
Copyright
2000,
American Mathematical Society
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