On set-valued cone absolutely summing maps

Coenraad Labuschagne; Valeria Marraffa

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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 $H_{ϕ} (μ) {\tilde{\otimes}}_{l} Y$ 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 $(H_{ϕ} (μ) {\tilde{\otimes}}_{l} Y) *$ and $H_{ϕ} (μ) * {\tilde{\otimes}}_{l} Y *$ in terms of the Radon-Nikodým property on Y. Convergence of norm-bounded martingales in H φ(μ, Y) is characterized in terms of...

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