Linear operators associated with p-Dunford, p-Pettis and p-Bochner integrable functions with values in a Banach space

In the present paper, we study several aspects of linear operators associated with p-Bochner, p-Dunford and p-Pettis integrable functions defined on a finite measure space with values in a Banach space. Continuity and compactness properties of said operators are discussed in details. We investigate...

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Published in:Journal of mathematical analysis and applications 2022-10, Vol.514 (1), p.126269, Article 126269
Main Authors: Mondal, Pratikshan, Dey, Lakshmi Kanta, Ali, Sk. Jaker
Format: Article
Language:English
Subjects:
[formula omitted]-Bochner representable
Collectively compact set
Equicompact set
p-Bochner integrable function
p-Dunford integrable function
p-Pettis integrable function
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description In the present paper, we study several aspects of linear operators associated with p-Bochner, p-Dunford and p-Pettis integrable functions defined on a finite measure space with values in a Banach space. Continuity and compactness properties of said operators are discussed in details. We investigate the operators in the light of p-summingness and order boundedness. We study p′-Pettis representability and p′-Bochner representability of an operator T∈L(Lp(μ),X), p∈(1,∞). Equicompactness and collective compactness of a family of linear operators associated with a family of integrable functions are also studied. Some results on equicompactness and collective compactness are obtained in the sequel.
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subjects [formula omitted]-Bochner representable
Collectively compact set
Equicompact set
p-Bochner integrable function
p-Dunford integrable function
p-Pettis integrable function
title Linear operators associated with p-Dunford, p-Pettis and p-Bochner integrable functions with values in a Banach space
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