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.

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1999-05-26