Annals of Functional Analysis

Strong relatively compact Dunford–Pettis property in Banach lattices

Halimeh Ardakani and S. M. Sadegh Modarres Mosadegh

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Abstract

In this paper, the concept of the strong relatively compact Dunford–Pettis property (strong DPrcP) in Banach lattices is introduced and Banach lattices with the strong DPrcP are characterized. Next, by introducing the class of almost Dunford–Pettis completely continuous operators from an arbitrary Banach lattice E to another F, we give some properties of them related to some well-known classes of operators and, especially, some related to the strong DPrcP of the Banach lattice E.

Article information

Source
Ann. Funct. Anal., Volume 7, Number 2 (2016), 270-280.

Dates
Received: 10 April 2015
Accepted: 2 August 2015
First available in Project Euclid: 29 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.afa/1456754404

Digital Object Identifier
doi:10.1215/20088752-3475634

Mathematical Reviews number (MathSciNet)
MR3652768

Zentralblatt MATH identifier
1348.46022

Subjects
Primary: 46B42: Banach lattices [See also 46A40, 46B40]
Secondary: 46B50: Compactness in Banach (or normed) spaces 47B65: Positive operators and order-bounded operators

Keywords
almost Dunford–Pettis set Dunford–Pettis completely continuous operator relatively compact Dunford–Pettis property

Citation

Ardakani, Halimeh; Modarres Mosadegh, S. M. Sadegh. Strong relatively compact Dunford–Pettis property in Banach lattices. Ann. Funct. Anal. 7 (2016), no. 2, 270--280. doi:10.1215/20088752-3475634. https://projecteuclid.org/euclid.afa/1456754404


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