Vector measure duality and tensor product representations of spaces of vector measures
Author:
E. A. Sánchez Pérez
Journal:
Proc. Amer. Math. Soc. 132 (2004), 33193326
MSC (2000):
Primary 46E30; Secondary 46G10
Published electronically:
June 2, 2004
MathSciNet review:
2073308
Fulltext PDF Free Access
Abstract 
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Abstract: Let 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 integrable functions with respect to . In particular, we identify this space with the dual of a certain space of operators under reasonable restrictions for the vector measure .
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 5.
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 S. Oltra, E. A. Sánchez Pérez and O. Valero, Spaces of a positive vector measure and generalized Fourier coefficients, Rocky Mountain Math. J., to appear.
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 E. A. Sánchez Pérez, Compactness arguments for spaces of integrable functions with respect to a vector measure and factorization of operators through LebesgueBochner spaces, Illinois J. Math. 45 (2001), 907923. MR 2003d:46055
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Additional Information
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
Email:
easancpe@mat.upv.es
DOI:
http://dx.doi.org/10.1090/S0002993904075215
PII:
S 00029939(04)075215
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. TomczakJaegermann
Article copyright:
© Copyright 2004 American Mathematical Society
