  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.
