## Annals of Functional Analysis

- Ann. Funct. Anal.
- Volume 9, Number 1 (2018), 123-136.

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

Mohammad B. Dehghani and S. Mohammad Moshtaghioun

#### Abstract

We introduce the notion of the $p$-Schur property ($1\le p\le \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., Volume 9, Number 1 (2018), 123-136.

**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

**Mathematical Reviews number (MathSciNet)**

MR3758748

**Zentralblatt MATH identifier**

06841346

**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. 9 (2018), no. 1, 123--136. doi:10.1215/20088752-2017-0033. https://projecteuclid.org/euclid.afa/1507169077