Annals of Functional Analysis
- Ann. Funct. Anal. (2017), 14 pages.
On the $p$-Schur property of Banach spaces
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.
Ann. Funct. Anal. (2017), 14 pages.
Received: 25 June 2016
Accepted: 8 March 2017
First available in Project Euclid: 5 October 2017
Permanent link to this document
Digital Object Identifier
Primary: 47L05: Linear spaces of operators [See also 46A32 and 46B28]
Secondary: 46B25: Classical Banach spaces in the general theory
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