  In this note we include two remarks about bounded ($\underline{not}$
necessarily contractive) linear projections on a von Neumann-algebra. We show
that if $M$ is a von Neumann-subalgebra of $B(H)$ which is complemented in B(H)
and isomorphic to $M \otimes M$ then $M$ is injective (or equivalently $M$ is
contractively complemented). We do not know how to get rid of the second
assumption on $M$. In the second part,we show that any complemented reflexive
subspace of a $C^*$- algebra is necessarily linearly isomorphic to a Hilbert
space.
