Higher order hyperexpansivity and higher order hypercontractivity

Hadi Obaid Alshammari; Hadi Obaid Alshammari

doi:10.3934/math.20231393

AIMS Mathematics

2023, Volume 8, Issue 11: 27227-27240. doi: 10.3934/math.20231393

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Higher order hyperexpansivity and higher order hypercontractivity

Hadi Obaid Alshammari ^,

Mathematics Department, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia

Received: 06 May 2023 Revised: 11 September 2023 Accepted: 17 September 2023 Published: 25 September 2023
MSC : 47B15, 47B20, 47A15

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.
- $ m $-isometric tuple,
- $ (m, p) $-isometric tuple,
- expansive operator,
- contractive operator
Citation: Hadi Obaid Alshammari. Higher order hyperexpansivity and higher order hypercontractivity[J]. AIMS Mathematics, 2023, 8(11): 27227-27240. doi: 10.3934/math.20231393

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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.

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