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

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 $(m,\mathrm{\infty })$-isometric operator tuples and study properties of and relations between these objects.