6533b853fe1ef96bd12ad346

RESEARCH PRODUCT

Spaces of Operator-valued Functions Measurable with Respect to the Strong Operator Topology

Oscar BlascoJan Van Neerven

subject

Operator (physics)010102 general mathematicsMathematical analysisBanach spaceCharacterization (mathematics)Space (mathematics)01 natural sciencesMeasure (mathematics)010101 applied mathematicsCombinatoricsBounded function0101 mathematicsMathematicsStrong operator topology

description

Let X and Y be Banach spaces and (Ω, Σ, μ) a finite measure space. In this note we introduce the space L p /μ; ℒ(X, Y)] consisting of all (equivalence classes of) functions Φ:Ω↦ℒ(X, Y) such that ω↦Φ(ω)x is strongly μ-measurable for all x∈X and ω↦Φ(ω)f(ω) belongs to L 1(μ; Y) for all f∈L p′ (μ; X), 1/p+1/p′=1. We show that functions in L p /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 p (μ; X) into L q (μ; Y), 1≤q<p<∞.

yearjournalcountryeditionlanguage
2009-01-01
https://doi.org/10.1007/978-3-0346-0211-2_6