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Extension of Riesz homomorphisms. III

Part of: Topological linear spaces and related structures

Published online by Cambridge University Press:  09 April 2009

Gerard Buskes
Gerard Buskes
Affiliation:
Department of Mathematics, University of Mississippi, University, Mississippi 38677, U.S.A.
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Abstract

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In this paper we prove an analogue of the separable version of Nachbin's characterization of injective Banach spaces in the setting of Banach lattices. The mappings involved are continuous Riesz homomorphisms defined on ideals of separable Banach lattices which can be extended to Riesz homomorphisms on the whole Banach lattice. We discuss applications to simultaneous extension operators and to extension of continuous mappings between certain topological spaces.

MSC classification

Secondary: 46A40: Ordered topological linear spaces, vector lattices
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 1 , August 1987 , pp. 35 - 46
Copyright
Copyright © Australian Mathematical Society 1987

References

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