Abstract

Let mm be a vector measure taking values in a Banach space XX. We prove that if the integration operator Im:L1(m)→XI_m: L^1(m) \to X, Im(f)=∫f dmI_m(f)=\int f \, dm, is completely continuous and XX is Asplund, then mm has finite variation and L1(m)=L1(∣m∣)L^1(m) =L^1(|m|).

Author information

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José M. Calabuig

Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain

jmcalabu@mat.upv.es

José Rodríguez

Departamento de Matemática Aplicada, Facultad de Informática, Universidad de Murcia, 30100 Espinardo (Murcia), Spain

joserr@um.es

Enrique A. Sánchez-Pérez

Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain

easancpe@mat.upv.es

Keywords

  • Integration operator
  • vector measure
  • completely continuous operator
  • Asplund space

Mathematics Subject Classification

46E30, 46G10, 47B07

References

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Suggested citation

J. M. Calabuig, J. Rodríguez, E. A. Sánchez-Pérez. “On Completely Continuous Integration Operators of a Vector Measure.” Journal of Convex Analysis 21 (2014), No. 3, 811–818. https://doi.org/10.68381/jca21043

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Published by Heldermann Verlag, 2014. Rights now held by Banach Press LLC.