an: Zbl 1194.46014
au: Alspach, Dale E.
ti: Good $\ell_2$-subspaces of $L_p$, $p>2$.
la: EN
so: Banach J. Math. Anal. 3, No. 2, 49-54, electronic only (2009).
py: 2009
dt: J
cc: *46B09 46B25 46E30
ut: subspaces of $L_p$; well complemented subspace; Hilbertian subspace; central
    limit theorem
ab: In a recent preprint, {\it R.\,Haydon, E.\,Odell}\/ and {\it
    Th.\,Schlumprecht} [``Small subspaces of $L_p$,'' \url{arXiv:0711.3919}]
    show that a Hilbertian subspace of $L_p$, $p>2$, contains a further subspace
    $Z$ that is $(1+\varepsilon)$-isomorphic to $\ell_2$ and complemented in
    $L_p$ by a projection of norm $\le (1+\varepsilon)\gamma_p$, where
    $\gamma_p$ is the $L_p$-norm of a standard Gaussian random variable. Their
    proof uses random measures and types \`a la Krivine and Maurey. Here, the
    author gives another proof that avoids these means and depends only on a
    version of the central limit theorem for martingales.
rv: Dirk Werner (Berlin)