The topological entropy of Banach spaces
Jozef Bobok, Henk Bruin

TL;DR
This paper explores the relationship between Banach spaces of real functions and topological entropy, revealing that certain subspaces contain functions with infinite entropy and constructing spaces with uniform entropy levels.
Contribution
It demonstrates that subspaces isometric to contain functions with infinite entropy and constructs one-dimensional Banach spaces where all nonzero functions share the same topological entropy.
Findings
Subspaces of C([0,1]) isometric to contain functions with infinite topological entropy
Constructed Banach spaces where all nonzero functions have a fixed topological entropy
Established links between Banach space structure and topological entropy values
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 which is isometrically isomorphic to contains a functions with infinite topological entropy. Also, for any , we construct a (one-dimensional) Banach space in which any nonzero function has topological entropy equal to .
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Taxonomy
TopicsAdvanced Banach Space Theory · Approximation Theory and Sequence Spaces · Optimization and Variational Analysis
