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

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A bounded linear operator T on a Banach space X is called an (m, p)-isometry if it satisfies the equation ∑ₖ₌₀ᵐ(-1)ᵏ m kTᵏxᵖ = 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.