EXTREME CONTRACTIONS IN $L\left( {\ell _2^p,\,\ell _2^q} \right)$ AND THE MAZUR INTERSECTION PROPERTY IN $\ell _2^p\,{ \otimes _\pi }\ell _2^q$

Abstract

In this paper, we show that the projective tensor product of a two-dimensional $\ell ^p$ 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 characterize the extreme contractions from $\ell _2^p$ to $\ell _2^q$ and obtain their closure.