<s>
The	O
ultrastrong	B-Algorithm
topology	I-Algorithm
is	O
similar	O
to	O
the	O
strong	O
(	O
operator	O
)	O
topology	O
.	O
</s>
<s>
For	O
example	O
,	O
on	O
any	O
norm-bounded	O
set	O
the	O
strong	O
operator	O
and	O
ultrastrong	B-Algorithm
topologies	I-Algorithm
are	O
the	O
same	O
.	O
</s>
<s>
The	O
ultrastrong	B-Algorithm
topology	I-Algorithm
is	O
stronger	O
than	O
the	O
strong	O
operator	O
topology	O
.	O
</s>
<s>
The	O
ultrastrong	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
ultrastrong	B-Algorithm
topology	I-Algorithm
is	O
better	O
than	O
the	O
strong	O
operator	O
topology	O
,	O
but	O
is	O
more	O
complicated	O
to	O
define	O
so	O
people	O
usually	O
use	O
the	O
strong	O
operator	O
topology	O
if	O
they	O
can	O
get	O
away	O
with	O
it	O
.	O
</s>
<s>
The	O
ultrastrong	B-Algorithm
topology	I-Algorithm
can	O
be	O
obtained	O
from	O
the	O
strong	O
operator	O
topology	O
as	O
follows	O
.	O
</s>
<s>
B(HH1 )	O
is	O
the	O
ultrastrong	B-Algorithm
topology	I-Algorithm
of	O
B(H )	O
.	O
</s>
<s>
The	O
adjoint	O
map	O
is	O
not	O
continuous	O
in	O
the	O
ultrastrong	B-Algorithm
topology	I-Algorithm
.	O
</s>
<s>
There	O
is	O
another	O
topology	O
called	O
the	O
ultrastrong*	O
topology	O
,	O
which	O
is	O
the	O
weakest	O
topology	O
stronger	O
than	O
the	O
ultrastrong	B-Algorithm
topology	I-Algorithm
such	O
that	O
the	O
adjoint	O
map	O
is	O
continuous	O
.	O
</s>
