On n-quasi-(m, q)-isometric operators on a Banach space

Abstract In this paper, we introduce the class of n-quasi-m-isometric operators on a Banach space. Such a class seems to be a natural generalization of m-isometric operators on Banach spaces and of n-quasi-m-isometric operators on Hilbert spaces. We start by giving some of their elementary properties, studying the products and the power of such operators. Next, we will explain the relation between C0-semigroups, n-quasi-(m, q)-isometric operators and (m, q)-isometric operators. Finally, we focus on the dynamic of an n-quasi-m-isometry. More precisely, we prove a result characterizing the supercyclicity of such a class.