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Media type:
E-Article
Title:
Extensions and Liftings of Positive Linear Mappings on Banach Lattices
Contributor:
Lotz, Heinrich P.
Published:
The American Mathematical Society, 1975
Published in:
Transactions of the American Mathematical Society, 211 (1975), Seite 85-100
Language:
English
ISSN:
0002-9947
Origination:
Footnote:
Description:
Let F be a closed sublattice of a Banach lattice G. We show that any positive linear mapping from F into L1(μ) 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.