This is an announcement for the paper "Octahedral norms in spaces of operators" by Julio Becerra Guerrero, Gines Lopez-Perez and Abraham Rueda Zoca.

Abstract: We study octahedral norms in the space of bounded linear operators between Banach spaces. In fact, we prove that $L(X,Y)$ has octahedral norm whenever $X^*$ and $Y$ have octahedral norm. As a consequence the space of operators $L(\ell_1 ,X)$ has octahedral norm if, and only if, $X$ has octahedral norm. These results also allows us to get the stability of strong diameter 2 property for projective tensor products of Banach spaces, which is an improvement of the known results about the size of nonempty relatively weakly open subsets in the unit ball of the projective tensor product of Banach spaces.

Archive classification: math.FA

Mathematics Subject Classification: 46B20, 46B22

Remarks: 16 pages

Submitted from: glopezp@ugr.es

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

http://front.math.ucdavis.edu/1407.6038

or

http://arXiv.org/abs/1407.6038