The notion of (p, r)-compactness

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Date

2019

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UNIVERSITE MOHAMED BOUDIAF - M’SILA FACULTE DES MATHEMATIQUES ET DE L’INFORMATIQUE

Abstract

bstract In this work we will interest by the notion of relatively compact sets, we go on to study the space of ( p ,r )-compact operators and describe its structure as an operator ideal. We introduce the concept of Lipschitz ( p ,r )-compact operators. We show that can be seen as a natural extension of the linear case and we transfer some properties of the linear case into the Lipschitz setting.

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Keywords

Compact operators, ( p ,r )-compact operators, Ideal operators, Lipschitz p-compact operators, Relatively ( p ,r )-compact subsets.

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