REFLEXIVITY FOR SPACES OF REGULAR OPERATORS ON BANACH LATTICES

We prove that if Banach lattices E and F are reflexive and each positive linear operator from E to F is compact then L-r( E; F), the space of all regular linear operators from E to F, is reflexive. Conversely, if E* or F has the bounded regular approximation property then the reflexivity of L-r( E; F) implies that each positive linear operator from E to F is compact. Analogously we also study the reflexivity for the space of regular multilinear operators on Banach lattices.