Dunford-Pettis operators on the space of Bochner integrable functions

• Autorzy: Marian Nowak
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46A70: Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)
• 46E40: Spaces of vector- and operator-valued functions
• 47B38: Operators on function spaces (general)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 95
• Numer: 1
• Strony: 353-358

Daty

wydano

2011

Twórcy

autor

Marian Nowak

• University of Zielona Góra, Faculty of Mathematics, Computer Science and Econometrics, ul. Prof. Szafrana 4A, 65-516 Zielona Góra, Poland

Identyfikatory

DOI

10.4064/bc95-0-21