<s>
In	O
mathematics	O
,	O
weak	B-Algorithm
convergence	I-Algorithm
in	O
a	O
Hilbert	O
space	O
is	O
convergence	B-Algorithm
of	O
a	O
sequence	O
of	O
points	O
in	O
the	O
weak	O
topology	O
.	O
</s>
<s>
is	O
sometimes	O
used	O
to	O
denote	O
this	O
kind	O
of	O
convergence	B-Algorithm
.	O
</s>
<s>
As	O
a	O
consequence	O
of	O
the	O
principle	O
of	O
uniform	O
boundedness	O
,	O
every	O
weakly	O
convergent	B-Algorithm
sequence	I-Algorithm
is	O
bounded	O
.	O
</s>
<s>
and	O
this	O
inequality	O
is	O
strict	O
whenever	O
the	O
convergence	B-Algorithm
is	O
not	O
strong	O
.	O
</s>
<s>
a	O
Euclidean	O
space	O
,	O
then	O
weak	O
and	O
strong	O
convergence	B-Algorithm
are	O
equivalent	O
.	O
</s>
<s>
tends	O
to	O
zero	O
for	O
any	O
square-integrable	B-Algorithm
function	I-Algorithm
on	O
when	O
goes	O
to	O
infinity	O
,	O
which	O
is	O
by	O
Riemann	O
–	O
Lebesgue	O
lemma	O
,	O
i.e.	O
</s>
<s>
This	O
dissimilarity	O
is	O
one	O
of	O
the	O
reasons	O
why	O
this	O
type	O
of	O
convergence	B-Algorithm
is	O
considered	O
to	O
be	O
"	O
weak.	O
"	O
</s>
<s>
The	O
definition	O
of	O
weak	B-Algorithm
convergence	I-Algorithm
can	O
be	O
extended	O
to	O
Banach	O
spaces	O
.	O
</s>
<s>
for	O
some	O
in	O
,	O
so	O
one	O
obtains	O
the	O
Hilbert	O
space	O
definition	O
of	O
weak	B-Algorithm
convergence	I-Algorithm
.	O
</s>
