Weakly compact holomorphic mappings on Banach spaces

Raymond Ryan
1988 Pacific Journal of Mathematics  
A holomorphic mapping /: E -> F of complex Banach spaces is weakly compact if every x e E has a neighbourhood V x such that f(V x ) is a relatively weakly compact subset of F. Several characterizations of weakly holomorphic mappings are given which are analogous to classical characterizations of weakly compact linear mappings and the Davis-Figiel-Johnson-Pelczynski factorization theorem is extended to weakly compact holomorphic mappings. It is shown that the complex Banach space E has the
more » ... ty that every holomorphic mapping from E into an arbitrary Banach space is weakly compact if and only if the space Jίf(E) of holomorphic complex-valued functions on E, endowed with the bornological topology τ δ , is reflexive.
doi:10.2140/pjm.1988.131.179 fatcat:dxcg3o7fzvg5vlzz4nhlwtmmre