This is an announcement for the paper "Subspaces of Banach spaces with big slices" by Julio Becerra Guerrero, Gines Lopez-Perez and Abraham Rueda.

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.

Archive classification: math.FA

Mathematics Subject Classification: 46B20, 46B22

Remarks: 12 pages

Submitted from: glopezp@ugr.es

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1410.4324

or

http://arXiv.org/abs/1410.4324