Higher order hyperexpansivity and higher order hypercontractivity

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...

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Main Author: Hadi Obaid Alshammari
Format: Article
Language:English
Published: AIMS Press 2023-09-01
Series:AIMS Mathematics
Subjects:
Online Access:https://www.aimspress.com/article/doi/10.3934/math.20231393?viewType=HTML
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author Hadi Obaid Alshammari
author_facet Hadi Obaid Alshammari
author_sort Hadi Obaid Alshammari
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description 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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spelling doaj.art-d407f77340454a55ab279ed9b3382a042023-10-16T01:25:20ZengAIMS PressAIMS Mathematics2473-69882023-09-01811272272724010.3934/math.20231393Higher order hyperexpansivity and higher order hypercontractivityHadi Obaid Alshammari0Mathematics Department, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi ArabiaAs 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.https://www.aimspress.com/article/doi/10.3934/math.20231393?viewType=HTMLm-isometric tuple(m,p)-isometric tupleexpansive operatorcontractive operator
spellingShingle Hadi Obaid Alshammari
Higher order hyperexpansivity and higher order hypercontractivity
AIMS Mathematics
m-isometric tuple
(m,p)-isometric tuple
expansive operator
contractive operator
title Higher order hyperexpansivity and higher order hypercontractivity
title_full Higher order hyperexpansivity and higher order hypercontractivity
title_fullStr Higher order hyperexpansivity and higher order hypercontractivity
title_full_unstemmed Higher order hyperexpansivity and higher order hypercontractivity
title_short Higher order hyperexpansivity and higher order hypercontractivity
title_sort higher order hyperexpansivity and higher order hypercontractivity
topic m-isometric tuple
(m,p)-isometric tuple
expansive operator
contractive operator
url https://www.aimspress.com/article/doi/10.3934/math.20231393?viewType=HTML
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