Annals of Functional Analysis

On the p-Schur property of Banach spaces

Mohammad B. Dehghani and S. Mohammad Moshtaghioun

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Abstract

We introduce the notion of the p-Schur property (1p) as a generalization of the Schur property of Banach spaces, and then we present a number of basic properties and some examples. We also study its relation with some geometric properties of Banach spaces, such as the Gelfand–Phillips property. Moreover, we verify some necessary and sufficient conditions for the p-Schur property of some closed subspaces of operator spaces.

Article information

Source
Ann. Funct. Anal. (2017), 14 pages.

Dates
Received: 25 June 2016
Accepted: 8 March 2017
First available in Project Euclid: 5 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.afa/1507169077

Digital Object Identifier
doi:10.1215/20088752-2017-0033

Subjects
Primary: 47L05: Linear spaces of operators [See also 46A32 and 46B28]
Secondary: 46B25: Classical Banach spaces in the general theory

Keywords
Gelfand–Phillips property Schur property weakly p-compact set weakly p-convergent sequence

Citation

Dehghani, Mohammad B.; Moshtaghioun, S. Mohammad. On the $p$ -Schur property of Banach spaces. Ann. Funct. Anal., advance publication, 5 October 2017. doi:10.1215/20088752-2017-0033. https://projecteuclid.org/euclid.afa/1507169077


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