The topological entropy of Banach spaces

Jozef Bobok, Henk Bruin

Published 2011-06-01Version 1

We investigate some properties of (universal) Banach spaces of real functions in the context of topological entropy. Among other things, we show that any subspace of $C([0,1])$ which is isometrically isomorphic to $\ell_1$ contains a functions with infinite topological entropy. Also, for any $t \in [0, \infty]$, we construct a (one-dimensional) Banach space in which any nonzero function has topological entropy equal to $t$.