Open Access
October 2016 Subspaces of Banach spaces with big slices
Julio Becerra Guerrero, Ginés López-Pérez, Abraham Rueda Zoca
Banach J. Math. Anal. 10(4): 771-782 (October 2016). DOI: 10.1215/17358787-3649392


We study when diameter 2 properties can be inherited by subspaces. We obtain that the slice diameter 2 property (resp., the diameter 2 property, strong diameter 2 property) passes from a Banach space X to a subspace Y whenever X/Y is finite-dimensional and Y is complemented by a norm 1 projection (resp., the quotient X/Y is finite-dimensional and strongly regular). Also, we study the same problem for the dual properties of diameter 2 properties, such as having octahedral, weakly octahedral, or 2-rough norm.


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Julio Becerra Guerrero. Ginés López-Pérez. Abraham Rueda Zoca. "Subspaces of Banach spaces with big slices." Banach J. Math. Anal. 10 (4) 771 - 782, October 2016.


Received: 8 October 2015; Accepted: 12 January 2016; Published: October 2016
First available in Project Euclid: 20 September 2016

zbMATH: 1365.46007
MathSciNet: MR3548625
Digital Object Identifier: 10.1215/17358787-3649392

Primary: 46B04
Secondary: 46B22 , 52A10

Keywords: diameter $2$ properties , diameter-two properties , octahedral norms , slices

Rights: Copyright © 2016 Tusi Mathematical Research Group

Vol.10 • No. 4 • October 2016
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