Powers of m-isometries (original) (raw)

Abstract

A bounded linear operator T on a Banach space X is called an (m, p)-isometry for a positive integer m and a real number p ≥ 1 if, for any

Key takeaways

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  1. Any power of an (m, p)-isometry remains an (m, p)-isometry (Theorem 3.1).
  2. Operators with some powers as m-isometries belong to the same class (Theorem 3.6).
  3. The class of m-isometries is stable under powers, enhancing existing results.
  4. Recursive equations are pivotal for deriving properties of m-isometries.
  5. Corollary 3.7 provides specific cases where T is an (m, p)-isometry.

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