The topological entropy of Banach spaces
Jozef Bobok, Henk Bruin · The Journal of Difference Equations and Applications · 2011
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 ℓ1 contains a function with infinite topological entropy. Also, for any t ∈ [0,∞], we construct a (one-dimensional) Banach space in which any non-zero function has topological entropy equal to t.