Equivalence of multi-norms

TL;DR

This paper systematically investigates the conditions under which different pairs of multi-norms are mutually equivalent, advancing the theoretical understanding of multi-norm structures.

Contribution

It provides a comprehensive analysis of the equivalence relations among various multi-norms, building on foundational definitions by Dales and Polyakov.

Findings

Characterization of when multi-norms are mutually equivalent

Identification of key properties influencing equivalence

Extension of the theory of multi-norms

Abstract

The theory of multi-norms was developed by H.\ G.\ Dales and M.\ E.\ Polyakov in a memoir that was published in \emph{Dissertationes Mathematicae}. In that memoir, the notion of `equivalence' of multi-norms was defined. In the present memoir, we make a systematic study of when various pairs of multi-norms are mutually equivalent.