Annals of Functional Analysis

On the modulus of disjointness-preserving operators and b-AM-compact operators on Banach lattices

Kazem Haghnezhad Azar and Razi Alavizadeh

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Abstract

We study several properties of the modulus of order bounded disjointness-preserving operators. We show that, if T is an order bounded disjointness-preserving operator, then T and |T| have the same compactness property for several types of compactness. Finally, we characterize Banach lattices having b-AM-compact (resp., AM-compact) operators defined between them as having a modulus that is b-AM-compact (resp., AM-compact).

Article information

Source
Ann. Funct. Anal., Volume 9, Number 1 (2018), 101-110.

Dates
Received: 7 February 2017
Accepted: 27 February 2017
First available in Project Euclid: 14 August 2017

Permanent link to this document
https://projecteuclid.org/euclid.afa/1502697620

Digital Object Identifier
doi:10.1215/20088752-2017-0027

Mathematical Reviews number (MathSciNet)
MR3758746

Zentralblatt MATH identifier
06841344

Subjects
Primary: 46B42: Banach lattices [See also 46A40, 46B40]
Secondary: 47B60: Operators on ordered spaces

Keywords
modulus disjointness-preserving b-AM-compact AM-compact

Citation

Haghnezhad Azar, Kazem; Alavizadeh, Razi. On the modulus of disjointness-preserving operators and $b$ - $AM$ -compact operators on Banach lattices. Ann. Funct. Anal. 9 (2018), no. 1, 101--110. doi:10.1215/20088752-2017-0027. https://projecteuclid.org/euclid.afa/1502697620


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