Some properties of $ n $-quasi-$ (m, q) $-isometric operators on a Banach space

Abstract

In this paper, we introduced the class of $ n $-quasi-$ (m, q) $-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 started by giving some of their elementary properties and studying the products and the power of such operators. Next, we focused on the dynamic of a $ n $-quasi-$ m $-isometry. More precisely, we proved a result by characterizing the supercyclicity of such a class.

Keywords

• $ m $-isometry
• $ (m
• q) $-isometry
• $ n $-quasi-$ m $-isometry
• $ \mathcal{c}_0 $-semigroup