OPTIMAL EXTENSIONS FOR POSITIVE ORDER CONTINUOUS OPERATORS ON BANACH FUNCTION SPACES
Glasgow mathematical journal, Tome 56 (2014) no. 3, pp. 481-501
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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.
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
@article{10_1017_S0017089513000384,
author = {DELGADO, O.},
title = {OPTIMAL {EXTENSIONS} {FOR} {POSITIVE} {ORDER} {CONTINUOUS} {OPERATORS} {ON} {BANACH} {FUNCTION} {SPACES}},
journal = {Glasgow mathematical journal},
pages = {481--501},
year = {2014},
volume = {56},
number = {3},
doi = {10.1017/S0017089513000384},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000384/}
}
TY - JOUR AU - DELGADO, O. TI - OPTIMAL EXTENSIONS FOR POSITIVE ORDER CONTINUOUS OPERATORS ON BANACH FUNCTION SPACES JO - Glasgow mathematical journal PY - 2014 SP - 481 EP - 501 VL - 56 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000384/ DO - 10.1017/S0017089513000384 ID - 10_1017_S0017089513000384 ER -
%0 Journal Article %A DELGADO, O. %T OPTIMAL EXTENSIONS FOR POSITIVE ORDER CONTINUOUS OPERATORS ON BANACH FUNCTION SPACES %J Glasgow mathematical journal %D 2014 %P 481-501 %V 56 %N 3 %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000384/ %R 10.1017/S0017089513000384 %F 10_1017_S0017089513000384
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