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 .

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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:
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