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Metric Entropy of Convex Hulls in Banach Spaces
Author(s) -
Carl Bernd,
Kyrezi Ioanna,
Pajor Alain
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799008005
Subject(s) - mathematics , banach space , convex hull , regular polygon , hilbert space , hull , metric space , entropy (arrow of time) , pure mathematics , uniformly convex space , combinatorics , discrete mathematics , banach manifold , lp space , geometry , physics , quantum mechanics , marine engineering , engineering
The paper presents diverse methods for estimating the covering number of a precompact subset of a Banach space when the entropy of the set of its extremal points is already known. In the case of a Hilbert space, the Gelfand diameters of the subset are also estimated.