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Zeitschrift für Analysis und ihre Anwendungen


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Volume 3, Issue 3, 1984, pp. 245–262
DOI: 10.4171/ZAA/105

Published online: 1984-06-30

Lokale Reflexivität und lokale Dualität von Ultraprodukten für halbgeordnete Banachräume

Klaus-Detlef Kürsten[1]

(1) Universität Leipzig, Germany

Let $(E_i)_U$ be the ultraproduct of ordered Banach spaces and let $L$ be a finite dimensional sub-space of the dual $(E_i)_u*$. Then there exists a positive iscmetric imbedding of $L$ into $(E_i*)_U$ 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 $E**$ into $E$ which exist by the principle of local reflexivity.

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Kürsten Klaus-Detlef: Lokale Reflexivität und lokale Dualität von Ultraprodukten für halbgeordnete Banachräume. Z. Anal. Anwend. 3 (1984), 245-262. doi: 10.4171/ZAA/105