Lokale Reflexivität und lokale Dualität von Ultraprodukten für halbgeordnete Banachräume

Abstract

Let $(E_i{)}_U$ be the ultraproduct of ordered Banach spaces and let $L$ be a finite dimensional sub-space of the dual $(E_i{)}_u^{\ast }$. Then there exists a positive iscmetric imbedding of $L$ into $(E_i^{\ast }{)}_U$ also satisfying some additional conditions In the case of Banach lattices the isometric imbedding may be chosen as a lattice homomorphism. Similar but somewhat weaker positivity properties can be satisfied for the almost isometric imbeddings of finite dimensional subspaces of $E^{\ast \ast }$ into $E$ which exist by the principle of local reflexivity.