Extreme contractions in ${\cal L}(\ell^p_2, \ell^q_2)$ and the mazur intersection property in $\ell^p_2 \otimes_{\p} \ell^q_2$

Abstract

In this paper, we show that the projective tensor product of a two-dimen\-sional $\ell^p$ space with a two-dimensional $\ell^q$ space never has the Mazur Intersection Property for a large range of values of $p$ and $q$. For this purpose, we characterise the extreme contractions from $\ell^p_2$ to $\ell^q_2$ and obtain their closure.