Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4673044 | Indagationes Mathematicae | 2012 | 10 Pages |
Abstract
Let ΣΣ be a σσ-algebra of subsets of a non-empty set ΩΩ. Let B(Σ)B(Σ) be the Banach lattice of all bounded ΣΣ-measurable real-valued functions defined on ΩΩ, equipped with the natural Mackey topology τ(B(Σ),ca(Σ))τ(B(Σ),ca(Σ)). We study (τ(B(Σ),ca(Σ)),ξ)(τ(B(Σ),ca(Σ)),ξ)-continuous linear operators from B(Σ)B(Σ) to a quasicomplete locally convex space (E,ξ)(E,ξ). A generalized Nikodym convergence theorem and a Vitali–Hahn–Saks type theorem for operators on B(Σ)B(Σ) are obtained. It is shown that the space (B(Σ),τ(B(Σ),ca(Σ)))(B(Σ),τ(B(Σ),ca(Σ))) has the strict Dunford–Pettis property. Moreover, a Yosida–Hewitt type decomposition for weakly compact operators on B(Σ)B(Σ) is given.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Marian Nowak,