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February 2018 On the p-Schur property of Banach spaces
Mohammad B. Dehghani, S. Mohammad Moshtaghioun
Ann. Funct. Anal. 9(1): 123-136 (February 2018). DOI: 10.1215/20088752-2017-0033

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.

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Mohammad B. Dehghani. S. Mohammad Moshtaghioun. "On the p-Schur property of Banach spaces." Ann. Funct. Anal. 9 (1) 123 - 136, February 2018. https://doi.org/10.1215/20088752-2017-0033

Information

Received: 25 June 2016; Accepted: 8 March 2017; Published: February 2018
First available in Project Euclid: 5 October 2017

zbMATH: 06841346
MathSciNet: MR3758748
Digital Object Identifier: 10.1215/20088752-2017-0033

Subjects:
Primary: 47L05
Secondary: 46B25

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

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.9 • No. 1 • February 2018
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