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

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.