Spaces of Operator-valued Functions Measurable with Respect to the Strong Operator Topology
نویسنده
چکیده
Let X and Y be Banach spaces and (Ω,Σ, μ) a finite measure space. In this note we introduce the space L[μ;L (X, Y )] consisting of all (equivalence classes of) functions Φ : Ω 7→ L (X, Y ) such that ω 7→ Φ(ω)x is strongly μ-measurable for all x ∈ X and ω 7→ Φ(ω)f(ω) belongs to L(μ; Y ) for all f ∈ L ′ (μ;X), 1/p + 1/p = 1. We show that functions in L[μ;L (X, Y )] define operator-valued measures with bounded p-variation and use these spaces to obtain an isometric characterization of the space of all L (X, Y )-valued multipliers acting boundedly from L(μ;X) into L(μ; Y ), 1 6 q < p < ∞.
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تاریخ انتشار 2009