The topological entropy of Banach spaces

Jozef Bobok; Henk Bruin

The topological entropy of Banach spaces

Dynamical Systems 2011-06-02 v1

Authors: Jozef Bobok , Henk Bruin

Abstract

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 $t$ .

Keywords

topological entropy Banach spaces real functions isometric isomorphism ℓ₁ space

Cite

@article{arxiv.1106.0111,
  title  = {The topological entropy of Banach spaces},
  author = {Jozef Bobok and Henk Bruin},
  journal= {arXiv preprint arXiv:1106.0111},
  year   = {2011}
}

Comments

The paper is going to appear at Journal of Difference Equations and Applications

The topological entropy of Banach spaces

Abstract

Keywords

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