RT Journal Article
T1 On completion of spaces of weakly continuous functions.
A1 Ferrera Cuesta, Juan
A1 Gómez Gil, Javier
A1 Llavona, José G.
AB Let E  and F  be two Banach spaces and let A  be a nonempty subset of E . A mapping f:A→F  is said to be weakly continuous if it is continuous when A  has the relative weak topology and F  has the topology of its norm. Let A={E} , B=  {A⊂E:A  is bounded} and C=  {A⊂E:A  is weakly compact}. Then C w (E;F) , C wb (E;F)  and C wk (E;F)  are the spaces of all mappings f:E→F  whose restrictions to subsets A⊂E  belonging to A , B  and C , respectively, are weakly continuous. Clearly, C w (E;F)⊂C wb (E;F)⊂C wk (E;F) , and they are all endowed with the topology of uniform convergence on weakly compact subsets of E . The authors show that C wk (E;F)  is the completion of C w (E;F) . They also show that, when E  has no subspace isomorphic to l 1  , then C wb (E;F)=C wk (E;F) . When E  has the Dunford-Pettis property and contains a subspace isomorphic to l 1  , the authors prove that C wb (E;F)  is a proper subspace of C wk (E;F) . The same conclusion holds when E  is a Banach space that contains a subspace isomorphic to l ∞  .
PB LONDON MATH SOC
SN 0024-6093
YR 1983
FD 1983
LK https://hdl.handle.net/20.500.14352/64622
UL https://hdl.handle.net/20.500.14352/64622
LA eng
DS Docta Complutense
RD 11 abr 2025