<s>
The	O
finest	O
locally	B-Algorithm
convex	I-Algorithm
topological	I-Algorithm
vector	I-Algorithm
space	I-Algorithm
(	O
TVS	O
)	O
topology	O
on	O
the	O
tensor	O
product	O
of	O
two	O
locally	B-Algorithm
convex	I-Algorithm
TVSs	O
,	O
making	O
the	O
canonical	O
map	O
(	O
defined	O
by	O
sending	O
to	O
)	O
continuous	O
is	O
called	O
the	O
inductive	O
topology	O
or	O
the	O
-topology	O
.	O
</s>
<s>
Throughout	O
let	O
and	O
be	O
locally	B-Algorithm
convex	I-Algorithm
topological	I-Algorithm
vector	I-Algorithm
spaces	I-Algorithm
and	O
be	O
a	O
linear	O
map	O
.	O
</s>
<s>
The	O
set	O
of	O
continuous	B-Algorithm
linear	I-Algorithm
maps	I-Algorithm
(	O
resp	O
.	O
</s>
<s>
If	O
is	O
any	O
continuous	B-Algorithm
linear	I-Algorithm
map	I-Algorithm
between	O
Hilbert	O
spaces	O
,	O
then	O
is	O
always	O
positive	O
.	O
</s>
<s>
If	O
is	O
a	O
locally	B-Algorithm
convex	I-Algorithm
TVS	O
topology	O
on	O
(	O
with	O
this	O
topology	O
will	O
be	O
denoted	O
by	O
)	O
,	O
then	O
is	O
equal	O
to	O
the	O
inductive	B-Algorithm
tensor	I-Algorithm
product	I-Algorithm
topology	O
if	O
and	O
only	O
if	O
it	O
has	O
the	O
following	O
property	O
:	O
</s>
