A description of Banach space-valued Orlicz hearts

• Autorzy: Coenraad Labuschagne , Theresa Offwood
• Języki publikacji: EN

Abstrakty

EN

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 $$ H_\varphi \left( \mu \right)\tilde \otimes _l Y $$ 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 $$ \left( {H_\varphi \left( \mu \right)\tilde \otimes _l Y} \right)* $$ and $$ H_\varphi \left( \mu \right)*\tilde \otimes _l Y* $$ in terms of the Radon-Nikodým property on Y. Convergence of norm-bounded martingales in H φ(μ, Y) is characterized in terms of the Radon-Nikodým property on Y. Using the associativity of the l-norm, an alternative proof is given of the known fact that for any separable Banach lattice E and any Banach space Y, E and Y have the Radon-Nikodým property if and only if $$ E\tilde \otimes _l Y $$ has the Radon-Nikodým property. As a corollary, the Radon-Nikodým property in H φ(μ, Y) is described in terms of the Radon-Nikodým property on H φ(μ) and Y.

Słowa kluczowe

EN

Bochner norm; l-norm; Banach lattice; Banach space; Martingale; Orlicz space; Orlicz heart; Tensor product; Radon-Nikodým property

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 6
• Strony: 1109-1119

Daty

wydano

2010-12-01

online

2010-10-30

Twórcy

autor

Coenraad Labuschagne

• University of the Witwatersrand,

autor

Theresa Offwood

• University of the Witwatersrand,

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Identyfikatory

DOI

10.2478/s11533-010-0065-9