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

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

1994-12-12

arxiv.org/abs/math/9412213v1

Mathematics

Functional Analysis

Scientific paper

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.

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