Absolutely continuous linear operators on Köthe-Bochner spaces

• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46E40: Spaces of vector- and operator-valued functions
• 47B38: Operators on function spaces (general)
• 46A20: Duality theory
• 47B07: Operators defined by compactness properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 92
• Numer: 1
• Strony: 85-89

Daty

wydano

2011

Twórcy

Identyfikatory

DOI

10.4064/bc92-0-6