Absolutely continuous linear operators on Köthe-Bochner spaces

"Absolutely continuous linear operators on Köthe-Bochner spaces." Banach Center Publications 92.1 (2011): 85-89. <http://eudml.org/doc/282496>.

@article{Unknown2011,
abstract = {Let E be a Banach function space over a finite and atomless measure space (Ω,Σ,μ) and let $(X,||·||_X)$ and $(Y,||·||_Y)$ be real Banach spaces. A linear operator T acting from the Köthe-Bochner space E(X) to Y is said to be absolutely continuous if $||T(1_\{Aₙ\}f)||_Y → 0$ whenever μ(Aₙ) → 0, (Aₙ) ⊂ Σ. In this paper we examine absolutely continuous operators from E(X) to Y. Moreover, we establish relationships between different classes of linear operators from E(X) to Y.},
journal = {Banach Center Publications},
keywords = {Köthe-Bochner spaces; absolutely continuous operators; smooth operators; -smooth operators; order bounded operators; order weakly compact operators},
language = {eng},
number = {1},
pages = {85-89},
title = {Absolutely continuous linear operators on Köthe-Bochner spaces},
url = {http://eudml.org/doc/282496},
volume = {92},
year = {2011},
}

TY - JOUR
TI - Absolutely continuous linear operators on Köthe-Bochner spaces
JO - Banach Center Publications
PY - 2011
VL - 92
IS - 1
SP - 85
EP - 89
AB - Let E be a Banach function space over a finite and atomless measure space (Ω,Σ,μ) and let $(X,||·||_X)$ and $(Y,||·||_Y)$ be real Banach spaces. A linear operator T acting from the Köthe-Bochner space E(X) to Y is said to be absolutely continuous if $||T(1_{Aₙ}f)||_Y → 0$ whenever μ(Aₙ) → 0, (Aₙ) ⊂ Σ. In this paper we examine absolutely continuous operators from E(X) to Y. Moreover, we establish relationships between different classes of linear operators from E(X) to Y.
LA - eng
KW - Köthe-Bochner spaces; absolutely continuous operators; smooth operators; -smooth operators; order bounded operators; order weakly compact operators
UR - http://eudml.org/doc/282496
ER -