On the second parameter of an (m, p)-isometry

A bounded linear operator T on a Banach space X is called an (m, p)-isometry if it satisfies the equation ∑mk=0(−1)k(mk)||p=0, for all x ∈ X. In this paper we study the structure which underlies the second parameter of (m, p)-isometric operators. We concentrate on determining when an (m, p)-isometry is a (μ, q)-isometry for some pair (μ, q). We also extend the definition of (m, p)-isometry, to include p = ∞ and study basic properties of these (m,∞)-isometries