  We are interested in the question when a Banach space $X$ with an
unconditional basis is isomorphic (as a Banach space) to an order-continuous
nonatomic Banach lattice. We show that this is the case if and only if $X$ is
isomorphic as a Banach space with $X(\ell_2)$. This and results of J. Bourgain
are used to show that spaces $H_1(\bold T^n)$ are not isomorphic to nonatomic
Banach lattices. We also show that tent spaces introduced in \cite{4} are
isomorphic to Rad $H_1$.
