Weak convergence is usually either denoted 
or 
. A sequence 
of vectors in an inner
product space 
is called weakly convergent to a vector in 
if
 |
Every strongly convergent sequence is also weakly convergent (but the opposite does not usually hold). This can be seen as follows.
Consider the sequence 
that converges strongly to 
, i.e., 
as 
. Schwarz's inequality
now gives
 |
The definition of weak convergence is therefore satisfied.
