Let
A
\mathcal A
be a reflexive algebra in Banach space
X
X
such that both
O
+
≠
O
O_+\not =O
and
X
−
≠
X
X_-\not =X
in
Lat
A
\operatorname {Lat}\,\mathcal A
, the invariant subspace lattice of
A
\mathcal A
, then every derivation of
A
\mathcal A
into itself is spatial. Furthermore, if
X
X
is additionally reflexive, then the set of all inner derivations of
A
\mathcal A
into itself is topologically algebraically reflexive.