## Annals of Functional Analysis

### On the $p$-Schur property of Banach spaces

#### Abstract

We introduce the notion of the $p$-Schur property ($1\leq p\leq\infty$) 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
Accepted: 8 March 2017
First available in Project Euclid: 5 October 2017

https://projecteuclid.org/euclid.afa/1507169077

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

#### 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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