Weak-strong continuity of multilinear mappings and the Pelczynski-Pitt theorem

[摘要] In generalizing a result of Pelczynski 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 l(p1) x ... x l(pN) into l(q) is compact if and only if Sigma(i=1)(n)(1/p(i)) < 1/q. (C) 1997 Academic Press.

[发布日期] 1997-02-15