Sie können Bookmarks mittels Listen verwalten, loggen Sie sich dafür bitte in Ihr SLUB Benutzerkonto ein.
Medientyp:
E-Artikel
Titel:
Extensions and liftings of positive linear mappings on Banach lattices
Beteiligte:
Lotz, Heinrich P.
Erschienen:
American Mathematical Society (AMS), 1975
Erschienen in:
Transactions of the American Mathematical Society, 211 (1975), Seite 85-100
Sprache:
Englisch
DOI:
10.1090/s0002-9947-1975-0383141-7
ISSN:
0002-9947;
1088-6850
Entstehung:
Anmerkungen:
Beschreibung:
Let F be a closed sublattice of a Banach lattice G. We show that any positive linear mapping from F into L 1 ( μ ) {L^1}(\mu ) or C ( X ) 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.