# Absolutely continuous linear operators on Köthe-Bochner spaces

Banach Center Publications (2011)

- Volume: 92, Issue: 1, page 85-89
- ISSN: 0137-6934

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top"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 -

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