  In this note, we answer a question raised by Johnson and Schechtman
\cite{JS}, about the hypercontractive semigroup on $\{-1,1\}^{\NN}$. More
generally, we prove the folllowing theorem. Let $1<p<2$. Let $(T(t))_{t>0}$ be
a holomorphic semigroup on $L_p$ (relative to a probability space). Assume the
following mild form of hypercontractivity: for some large enough number $s>0$,
$T(s)$ is bounded from $L_p$ to $L_2$. Then for any $t>0$, $T(t)$ is in the
norm closure in $B(L_p)$ (denoted by $\bar{\Gamma_2}$) of the subset (denoted
by ${\Gamma_2}$) formed by the operators mapping $L_p$ to $L_2$ (a fortiori
these operators factor through a Hilbert space).
