Higher order hyperexpansivity and higher order hypercontractivity

Abstract

As a natural extension of the concept of $ (m, p) $-hyperexpansive and $ (m, p) $-hypercontractive of a single operator, we introduce and study the concepts of $ (m, p) $-hyperexpansivity and $ (m, p) $-hypercontractivity for $ d $-tuple of commuting operators acting on Banach spaces. These concepts extend the definitions of $ m $-isometries and $ (m, p) $-isometric tuples of bounded linear operators acting on Hilbert or Banach spaces, which have been introduced and studied by many authors.

Keywords

• m-isometric tuple
• (m，p)-isometric tuple
• expansive operator
• contractive operator