Weighted shift and composition operators on ℓp which are (m,q)-isometries.

We obtain some conditions about the weighted shift and the composition operators on ℓ p to be ( m , q ) -isometries. In particular, we prove that if T is a strict ( 2 , q ) isometry, then p = q , whether T is a weighted shift or a composition operator on ℓ p . Moreover, we characterize the admissible weights for the weighted shift to be a strict ( 3 , p ) -isometry on ℓ p . The case of strict ( 4 , p ) -isometry is also studied. [ABSTRACT FROM AUTHOR]