Lokale Reflexivität und lokale Dualität von Ultraprodukten für halbgeordnete Banachräume (Q796791)

There are proved four (particularly known) theorems by similar methods. Each of these theorems states the finite representability of Banach spaces in certain subspaces, where several additional properties are satisfied. The first two theorems are versions of the principle of local reflexivity for ordered Banach spaces and for Banach lattices, respectively. The other theorems state in particular that any finite dimensional subspace of the dual of the ultraproduct of ordered Banach spaces admitts a positive isometric imbedding into the ultraproduct of the duals. In the case of Banach lattices this imbedding can be choosen to be a lattice isomorphism.