ON THE METRIC ENTROPY OF THE BANACH-MAZUR COMPACTUM Academic Article

abstract

• 2014 University College London. We study the metric entropy of the metric space Bn of all n-dimensional Banach spaces (the so-called Banach-Mazur compactum) equipped with the Banach-Mazur (multiplicative) distance d. We are interested either in estimates independent of the dimension or in asymptotic estimates when the dimension tends to . For instance, we prove that, if N(Bn,d,1+) is the smallest number of balls of radius 1+ that cover Bn, then for any >0 we have 0

authors

• Pisier, Gilles

published proceedings

• MATHEMATIKA

altmetric score

• 0.5

author list (cited authors)

• Pisier, G.

citation count

• 5

complete list of authors

• Pisier, Gilles

publication date

• January 2015

publisher

• Wiley  Publisher

published in

• Mathematika: a journal of pure and applied mathematics  Journal

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics
• 4902 Mathematical Physics
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.1112/S0025579314000102

start page

• 179

end page

• 198

volume

• 61

issue

• 1

URL

• http://dx.doi.org/10.1112/s0025579314000102