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

• 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
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2022.126269

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.