Weak]Strong Continuity of Multilinear Mappings and the Pełczy`nski]Pitt Theorem

In generalizing a result of Pełczy`nski the sequential weak to norm continuity of N-linear mappings between certain Banach spaces including spaces of type and cotype. will be studied. In particular, it is shown that every N-linear continuous mapping from lp1=???=lpN into lq is compact if and only if nis1 1rpi.-1rq.