Stabilizing isomorphisms from $\ell_p(\ell_2)$ into $L_p[0,1]$

Details Stabilizing isomorphisms from $\ell_p(\ell_2)$ into $L_p[0,1]$ Stabilizing isomorphisms from $\ell_p(\ell_2)$ into $L_p[0,1]$

2011-02-28

arxiv.org/abs/1103.0047v1

Mathematics

Functional Analysis

Scientific paper

Let $10$ and let $T:\ell_p(\ell_2)\overset{into}{\rightarrow}L_p[0,1]$ be an isomorphism. Then there is a subspace $Y\subset \ell_p(\ell_2)$ $(1+\epsilon)$-isomorphic to $\ell_p(\ell_2)$ such that: $T_{|Y}$ is an $(1+\epsilon)$-isomorphism and $T(Y)$ is $K_p$-complemented in $L_p[0,1]$, with $K_p$ depending only on $p$. Moreover, $K_p\le (1+\epsilon)\gamma_p$ if $p>2$ and $K_p\le (1+\epsilon)\gamma_{p/(p-1)}$ if $1

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