Banach Journal of Mathematical Analysis

The strong Gelfand–Phillips property in Banach lattices

Halimeh Ardakani, S. Mohammad Moshtaghioun, S. M. Sadegh Modarres Mosadegh, and Manijeh Salimi

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Abstract

We introduce the concept of the strong Gelfand–Phillips (GP) property in Banach lattices, and we characterize Banach lattices with the strong GP property. Next, by introducing the class of almost limited 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, to the strong GP property of the Banach lattice E.

Article information

Source
Banach J. Math. Anal., Volume 10, Number 1 (2016), 15-26.

Dates
Received: 6 December 2014
Accepted: 25 March 2015
First available in Project Euclid: 15 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1444913860

Digital Object Identifier
doi:10.1215/17358787-3158354

Mathematical Reviews number (MathSciNet)
MR3453521

Zentralblatt MATH identifier
1335.46013

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 limited set limited completely continuous operator Gelfand–Phillips property

Citation

Ardakani, Halimeh; Moshtaghioun, S. Mohammad; Modarres Mosadegh, S. M. Sadegh; Salimi, Manijeh. The strong Gelfand–Phillips property in Banach lattices. Banach J. Math. Anal. 10 (2016), no. 1, 15--26. doi:10.1215/17358787-3158354. https://projecteuclid.org/euclid.bjma/1444913860


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