$(m,p)$-isometric and $(m,\infty)$-isometric operator tuples on normed spaces

TL;DR

This paper introduces a new class of operator tuples called $(m,p)$-isometric and $(m, abla)$-isometric on normed spaces, extending existing concepts from Hilbert spaces and exploring their properties and relationships.

Contribution

It generalizes the concept of $m$-isometric operator tuples to normed spaces and introduces $(m, abla)$-isometric tuples, expanding the theoretical framework.

Findings

Defined $(m,p)$-isometric operator tuples on normed spaces

Extended the concept to include $(m, abla)$-isometric tuples

Analyzed properties and relations between these operator tuples

Abstract

We generalize the notion of $m$-isometric operator tuples on Hilbert spaces in a natural way to normed spaces. This is done by defining a tuple analogue of $(m,p)$-isometric operators, so-called $(m,p)$-isometric operator tuples. We then extend this definition further by introducing $(m,\infty)$-isometric operator tuples and study properties of and relations between these objects.