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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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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