  In this paper, we show that if the direct sum of two operators is
subspace-hypercyclic (satisfies subspace hypercyclic criterion), then both
operators are subspace-hypercyclic (satisfy subspace hypercyclic criterion).
Moreover, if an operator $T$ satisfies subspace-hypercyclic criterion, then so
$T\oplus T$ does. Also, we obtain that under certain conditions, if $T\oplus T$
is hypercyclic then $T$ satisfies subspace-hypercyclic criterion and, the
subspace-hypercyclic operators satisfy subspace-hypercyclic criterion which
gives the "subspace-hypercyclic" analogue of Theorem 2.3. (in Hereditarily
hypercyclic operators, J. Funct. Anal., 167:94--112, 1999 by P. B\'es and A.
Peris).
