Vector measure duality and tensor product representations of -spaces of vector measures
Author:
E. A. Sánchez Pérez
Journal:
Proc. Amer. Math. Soc. 132 (2004), 3319-3326
MSC (2000):
Primary 46E30; Secondary 46G10
DOI:
https://doi.org/10.1090/S0002-9939-04-07521-5
Published electronically:
June 2, 2004
MathSciNet review:
2073308
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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
.
- 1. R. G. Bartle, N. Dunford and J. Schwartz, Weak compactness and vector measures, Canad. J. Math. 7 (1955), 289-305. MR 16:1123c
- 2. A. Defant and K. Floret, Tensor norms and operator ideals, North-Holland Math. Studies, Amsterdam, 1993. MR 94e:46130
- 3.
G. P. Curbera, Operators into
of a vector measure and applications to Banach lattices, Math. Ann. 293 (1992), 317-330. MR 93b:46083
- 4.
G. P. Curbera, When
of a vector measure is an AL-space, Pacific J. Math. 162 (1994), 287-303. MR 94k:46070
- 5.
G. P. Curbera, Banach space properties of
of a vector measure, Proc. Amer. Math. Soc. 123 (1995), 3797-3806. MR 96b:46060
- 6. J. Diestel and J. J. Uhl, Vector Measures, Math. Surveys, vol. 15, Amer. Math. Soc., Providence, RI, 1977. MR 56:12216
- 7. L. M. García-Raffi, D. Ginestar and E. A. Sánchez Pérez. Integration with respect to a vector measure and function approximation, Abstract and Applied Analysis 5 (2000) 207-227. MR 2002k:41046
- 8. D. R. Lewis, Integration with respect to vector measures, Pacific J. Math. 33 (1970), 157-165. MR 41:3706
- 9. D. R. Lewis, On integrability and summability in vector spaces, Illinois J. Math. 16 (1972), 294-307. MR 45:502
- 10. J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Springer-Verlag, Berlin, 1977. MR 58:17766
- 11. J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II, Springer-Verlag, Berlin, 1979. MR 81c:46001
- 12.
S. Okada, The dual space of
of a vector measure
, J. Math. Anal. Appl. 177 (1993), 583-599. MR 94m:46050
- 13.
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.
- 14.
E. A. Sánchez Pérez, Compactness arguments for spaces of
-integrable functions with respect to a vector measure and factorization of operators through Lebesgue-Bochner spaces, Illinois J. Math. 45 (2001), 907-923. MR 2003d:46055
- 15.
E. A. Sánchez Pérez, Spaces of integrable functions with respect to vector measures of convex range and factorization of operators from
-spaces, Pacific J. Math. 207 (2002), 489-495.
- 16.
E. A. Sánchez Pérez, Vector measure orthonormal functions and best approximation for the
-norm, Arch. Math. 80 (2003), 177-190. MR 2004b:46034
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46E30, 46G10
Retrieve articles in all journals with MSC (2000): 46E30, 46G10
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:
https://doi.org/10.1090/S0002-9939-04-07521-5
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