Extreme contractions in $\mathcal{L}({\ell }_2^p,{\ell }_2^q)$ 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 ${\ell }_2^p$ to ${\ell }_2^q$ and obtain their closure.