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A description of Banach space-valued Orlicz hearts

Coenraad LabuschagneTheresa Offwood — 2010

Open Mathematics

Let Y be a Banach space, (Ω, Σ; μ) a probability space and φ a finite Young function. It is shown that the Y-valued Orlicz heart H φ(μ, Y) is isometrically isomorphic to the l-completed tensor product H ϕ μ ˜ l Y of the scalar-valued Orlicz heart Hφ(μ) and Y, in the sense of Chaney and Schaefer. As an application, a characterization is given of the equality of H ϕ μ ˜ l Y * and H ϕ μ * ˜ l Y * in terms of the Radon-Nikodým property on Y. Convergence of norm-bounded martingales in H φ(μ, Y) is characterized in terms of the Radon-Nikodým...

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