<s>
In	O
functional	B-Application
analysis	I-Application
,	O
a	O
branch	O
of	O
mathematics	O
,	O
the	O
ultraweak	B-Algorithm
topology	I-Algorithm
,	O
also	O
called	O
the	O
weak-*	O
topology	O
,	O
or	O
weak-*	O
operator	B-Algorithm
topology	I-Algorithm
or	O
σ-weak	O
topology	O
,	O
on	O
the	O
set	O
B(H )	O
of	O
bounded	O
operators	O
on	O
a	O
Hilbert	O
space	O
is	O
the	O
weak-*	O
topology	O
obtained	O
from	O
the	O
predual	O
B*( H	O
)	O
of	O
B(H )	O
,	O
the	O
trace	O
class	O
operators	O
on	O
H	O
.	O
In	O
other	O
words	O
it	O
is	O
the	O
weakest	O
topology	O
such	O
that	O
all	O
elements	O
of	O
the	O
predual	O
are	O
continuous	O
(	O
when	O
considered	O
as	O
functions	O
on	O
B(H )	O
)	O
.	O
</s>
<s>
The	O
ultraweak	B-Algorithm
topology	I-Algorithm
is	O
similar	O
to	O
the	O
weak	B-Algorithm
operator	I-Algorithm
topology	I-Algorithm
.	O
</s>
<s>
The	O
ultraweak	B-Algorithm
topology	I-Algorithm
is	O
stronger	O
than	O
the	O
weak	B-Algorithm
operator	I-Algorithm
topology	I-Algorithm
.	O
</s>
<s>
One	O
problem	O
with	O
the	O
weak	B-Algorithm
operator	I-Algorithm
topology	I-Algorithm
is	O
that	O
the	O
dual	O
of	O
B(H )	O
with	O
the	O
weak	B-Algorithm
operator	I-Algorithm
topology	I-Algorithm
is	O
"	O
too	O
small	O
"	O
.	O
</s>
<s>
The	O
ultraweak	B-Algorithm
topology	I-Algorithm
fixes	O
this	O
problem	O
:	O
the	O
dual	O
is	O
the	O
full	O
predual	O
B*( H	O
)	O
of	O
all	O
trace	O
class	O
operators	O
.	O
</s>
<s>
In	O
general	O
the	O
ultraweak	B-Algorithm
topology	I-Algorithm
is	O
more	O
useful	O
than	O
the	O
weak	B-Algorithm
operator	I-Algorithm
topology	I-Algorithm
,	O
but	O
it	O
is	O
more	O
complicated	O
to	O
define	O
,	O
and	O
the	O
weak	B-Algorithm
operator	I-Algorithm
topology	I-Algorithm
is	O
often	O
more	O
apparently	O
convenient	O
.	O
</s>
<s>
The	O
ultraweak	B-Algorithm
topology	I-Algorithm
can	O
be	O
obtained	O
from	O
the	O
weak	B-Algorithm
operator	I-Algorithm
topology	I-Algorithm
as	O
follows	O
.	O
</s>
<s>
Then	O
the	O
restriction	O
of	O
the	O
weak	B-Algorithm
operator	I-Algorithm
topology	I-Algorithm
on	O
B( H⊗H1	O
)	O
is	O
the	O
ultraweak	B-Algorithm
topology	I-Algorithm
of	O
B(H )	O
.	O
</s>
