Abstract

In this note we show that weakly compact operators from a Banach space $X$ into a complete (LB)-space $E$ need not factorize through a reflexive Banach space. If $E$ is a Fréchet space, then weakly compact operators from a Banach space $X$ into $E$ factorize through a reflexive Banach space. The factorization of operators from a Fréchet or a complete (LB)-space into a Banach space mapping bounded sets into relatively weakly compact sets is also investigated.

Keywords: Weakly compact operators; reflexive operators; factorization; reflexive Banach spaces; (LB)-spaces; Fréchet spaces.

MSC: 46A04, 46A03, 46A25, 46B10, 47B07

Pages:  330--335     

Volume  64 ,  Issue  4 ,  2012