Geodesic
OPTIMAL EXTENSIONS FOR POSITIVE ORDER CONTINUOUS OPERATORS ON BANACH FUNCTION SPACES
Glasgow mathematical journal, Tome 56 (2014) no. 3, pp. 481-501

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we give conditions under which a positive order continuous operator T defined on a Banach function space can be extended, preserving the order continuity in a certain optimal way. The optimal domain for T turns out to be a space of weakly integrable functions with respect to a vector measure (defined on a δ-ring) canonically associated to T. A similar result is obtained when T is σ-order continuous and we want to preserve the σ-order continuity. We apply these results to kernel operators.
DOI : 10.1017/S0017089513000384
Mots-clés : Primary 46G10, Secondary 46E30, 46B42 
DELGADO, O. OPTIMAL EXTENSIONS FOR POSITIVE ORDER CONTINUOUS OPERATORS ON BANACH FUNCTION SPACES. Glasgow mathematical journal, Tome 56 (2014) no. 3, pp. 481-501. doi: 10.1017/S0017089513000384
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