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Vector measure duality and tensor product representations of $L_p$-spaces of vector measures

Author: E. A. Sánchez Pérez
Journal: Proc. Amer. Math. Soc. 132 (2004), 3319-3326
MSC (2000): Primary 46E30; Secondary 46G10
Published electronically: June 2, 2004
MathSciNet review: 2073308
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Abstract: Let $\lambda$ be a countably additive vector measure. In this paper we use the definition of vector measure duality to establish a tensor product representation theorem for the space of $p$-integrable functions with respect to $\lambda$. In particular, we identify this space with the dual of a certain space of operators under reasonable restrictions for the vector measure $\lambda$.

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E. A. Sánchez Pérez
Affiliation: Departamento de Matemática Aplicada, E.T.S. Ingenieros de Caminos, Canales y Puertos, Universidad Politécnica de Valencia, Camino de Vera, 46071 Valencia, Spain

Keywords: Vector measures, $p$-integrable functions, tensor products
Received by editor(s): October 23, 2002
Received by editor(s) in revised form: August 21, 2003
Published electronically: June 2, 2004
Dedicated: The author dedicates this paper to the memory of Professor Klaus Floret.
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2004 American Mathematical Society