R. Alencar, K. Floret, eak-strong continuity of multilinear mappings and the Pe#lczynski-Pitt theorem, J. Math. Anal. Appl. 206 (1997), 532--549.  Home/Search   Document Not in Database   Summary   Related Articles

.... aturalin#FM : n# an d projection#c then id # n i=1 E i : # n i=1 E i I1 ##In ## n F # n F ## n,s F### n F n P1 ##Pn ## n i=1 E i (this co truction is, for n = 2, due toBon# j eris [BP an# was successively exten#DD to thepresen t form by Defan t Maestre [DM , AlF1an# Blasco [B1 ) 6KLAUSFLO R ET It follows that # n i=1 E i is isomorphic to a complemen ted subspace of # n,s F (with n atural mappin gs, which is importan t in view of the topological situation ) In particular: # n E is isomorphic to a complemen ted subspace of # n,s E n .IfE# ....

.... D = # n,s E # #P n (E) G # ; hen# (by what was just said) # n x# #(G, G #) con verges to # n x, i.e. for all q # G # = P n (E) q(x #) #q L , # n x## ##q L , # n x# = q(x) The space P n (E) is reflexive for example in the followin# cases: E = # p (if n p #; see [AlF1]an d [GoJ] or E = T , the orig in# l Tsirelson space (see [AAD] Note that the claim of the proposition holds also for then on reflexive space c 0sin#F all q #P n (c 0 ) are weaklysequen tially con tin uous (due to Bogdan owicz [Bo]an d Pe#lczyn# [Pe] see also [AlF1] a n# the boun#M ....

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R. Alencar, K. Floret, eak-strong continuity of multilinear mappings and the Pe#lczynski-Pitt theorem, J. Math. Anal. Appl. 206 (1997), 532--549.

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