This is an announcement for the paper "Basis entropy in Banach spaces" by Andrei Dorogovtsev and Mikhail Popov.
Abstract: We introduce and study two notions of entropy in a Banach space X with a normalized Schauder basis . The geometric entropy E(A) of a subset A of X is defined to be the infimum of radii of compact bricks containing A. We obtain several compactness characterizations for bricks (Theorem 3.7) useful for main results. We also obtain sufficient conditions on a set in a Hilbert space to have finite unconditional entropy. For Banach spaces without a Schauder basis we offer another entropy, called the Auerbach entropy. Finally, we pose some open problems.
Archive classification: math.FA
Mathematics Subject Classification: 46B50, 46B15, 60H07
Remarks: 22 pages
Submitted from: adoro@imath.kiev.ua
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.7248
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