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arXiv · 1410.4324

Subspaces of Banach spaces with big slices

Julio Becerra Guerrero·Ginés López-Pérez·Abraham Rueda Zoca
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Abstract

We study when diameter two properties pass down to subspaces. We obtain that the slice two property (respectively diameter two property, strong diameter two property) passes down from a Banach space $X$ to a subspace $Y$ whenever $Y$ is complemented by a norm one projection with finite-dimensional kernel (respectively the quotient $X/Y$ is finite dimensional, $X/Y$ is strongly regular). Also we study the same problem for dual properties of the above ones, as having octahedral, weakly octahedral or 2-rough norm.

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Julio Becerra Guerrero, Ginés López-Pérez, Abraham Rueda Zoca. 2014-10-16. Subspaces of Banach spaces with big slices. https://doi.org/10.1215/17358787-3649392

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