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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Extensions and liftings of positive linear mappings on Banach lattices


Author: Heinrich P. Lotz
Journal: Trans. Amer. Math. Soc. 211 (1975), 85-100
MSC: Primary 47B55; Secondary 46M10
MathSciNet review: 0383141
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Abstract: Let F be a closed sublattice of a Banach lattice G. We show that any positive linear mapping from F into $ {L^1}(\mu )$ or $ C(X)$ for a Stonian space X has a positive norm preserving extension to G. A dual result for positive norm preserving liftings is also established. These results are applied to obtain extension and lifting theorems for order summable and majorizing linear mappings. We also obtain some partial results concerning positive extensions and liftings of compact linear mappings.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0383141-7
Keywords: Extensions and liftings of positive linear mappings, injective Banach lattices, order summable mappings, majorizing mappings, tensor products of Banach lattices
Article copyright: © Copyright 1975 American Mathematical Society