On a H\"older covariant version of mean dimension

TL;DR

This paper introduces a modified version of mean dimension as an obstruction to the H"older conjugacy of l^p(G) and l^q(G) spaces under group actions, providing new insights into their structural relationship.

Contribution

It proposes a H"older covariant mean dimension concept that extends traditional mean dimension to analyze group actions on l^p spaces.

Findings

Modified mean dimension acts as an obstruction for H"older conjugacy.

Provides a new tool for studying group actions on Banach spaces.

Links mean dimension with H"older regularity in group representations.

Abstract

Let G be a infinite countable group which acts naturally on l^p(G). We introduce a modification of mean dimension which is an obstruction for l^p(G) and l^q(G) to be H\"older conjugates.