On inequivalences of sequences of characters
Volume 257 / 2021
Studia Mathematica 257 (2021), 241-252
MSC: Primary 42C10; Secondary 42A65.
DOI: 10.4064/sm190110-24-9
Published online: 11 December 2020
Abstract
We establish various results including the following: if $1 \lt p \lt \infty $ is not equal to $2$ and $\sigma $ is a bijection between the trigonometric functions on $[0,1)$ and the Walsh functions on $[0,1)$, then $\sigma $ does not extend to an isomorphism $L_p[0,1) \rightarrow L_p[0,1)$.
