Dunford-Pettis operators on the space of Bochner integrable functions

Marian Nowak. "Dunford-Pettis operators on the space of Bochner integrable functions." Banach Center Publications 95.1 (2011): 353-358. <http://eudml.org/doc/281614>.

@article{MarianNowak2011,
abstract = {Let (Ω,Σ,μ) be a finite measure space and let X be a real Banach space. Let $L^Φ(X)$ be the Orlicz-Bochner space defined by a Young function Φ. We study the relationships between Dunford-Pettis operators T from L¹(X) to a Banach space Y and the compactness properties of the operators T restricted to $L^Φ(X)$. In particular, it is shown that if X is a reflexive Banach space, then a bounded linear operator T:L¹(X) → Y is Dunford-Pettis if and only if T restricted to $L^∞(X)$ is $(τ(L^∞(X),L¹(X*)),||·||_Y)$-compact.},
author = {Marian Nowak},
journal = {Banach Center Publications},
keywords = {Orlicz-Bochner spaces; mixed topologies; generalized DF-spaces; Mackey topologies; Dunford-Pettis operators; compact operators},
language = {eng},
number = {1},
pages = {353-358},
title = {Dunford-Pettis operators on the space of Bochner integrable functions},
url = {http://eudml.org/doc/281614},
volume = {95},
year = {2011},
}

TY - JOUR
AU - Marian Nowak
TI - Dunford-Pettis operators on the space of Bochner integrable functions
JO - Banach Center Publications
PY - 2011
VL - 95
IS - 1
SP - 353
EP - 358
AB - Let (Ω,Σ,μ) be a finite measure space and let X be a real Banach space. Let $L^Φ(X)$ be the Orlicz-Bochner space defined by a Young function Φ. We study the relationships between Dunford-Pettis operators T from L¹(X) to a Banach space Y and the compactness properties of the operators T restricted to $L^Φ(X)$. In particular, it is shown that if X is a reflexive Banach space, then a bounded linear operator T:L¹(X) → Y is Dunford-Pettis if and only if T restricted to $L^∞(X)$ is $(τ(L^∞(X),L¹(X*)),||·||_Y)$-compact.
LA - eng
KW - Orlicz-Bochner spaces; mixed topologies; generalized DF-spaces; Mackey topologies; Dunford-Pettis operators; compact operators
UR - http://eudml.org/doc/281614
ER -