# Dunford-Pettis operators on the space of Bochner integrable functions

Banach Center Publications (2011)

- Volume: 95, Issue: 1, page 353-358
- ISSN: 0137-6934

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topMarian 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 -

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