This is an announcement for the paper "On the second parameter of an $(m, p)$-Isometry" by Philipp Hoffmann and Michael Mackey.

Abstract: A bounded linear operator $T$ on a Banach space $X$ is called an $(m, p)$-isometry if it satisfies the equation $\sum_{k=0}^{m}(-1)^{k} {m \choose k}|T^{k}x|^{p} = 0$, for all $x \in X$. In the first part of this paper we study the structure which underlies the second parameter of $(m, p)$-isometric operators. More precisely, we concentrate on the question of determining conditions on $q \neq p$ for which an $(m, p)$-isometry can be a $(\mu, q)$-isometry for some $\mu$. In the second part we extend the definition of $(m, p)$-isometry, to include $p=\infty$. We then study basic properties of these $(m, \infty)$-isometries.

Archive classification: math.FA

Submitted from: philipp.hoffmann@ucdconnect.ie

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1106.0339

or

http://arXiv.org/abs/1106.0339