A+ CATEGORY SCIENTIFIC UNIT

Lineability and spaceability on vector-measure spaces

Volume 219 / 2013

Giuseppina Barbieri, Francisco J. García-Pacheco, Daniele Puglisi Studia Mathematica 219 (2013), 155-161 MSC: Primary 28A33; Secondary 46E27. DOI: 10.4064/sm219-2-5

Abstract

It is proved that if $X$ is infinite-dimensional, then there exists an infinite-dimensional space of $X$-valued measures which have infinite variation on sets of positive Lebesgue measure. In term of spaceability, it is also shown that $ca(\mathcal {B}, \lambda , X) \setminus M_\sigma $, the measures with non-$\sigma $-finite variation, contains a closed subspace. Other considerations concern the space of vector measures whose range is neither closed nor convex. All of those results extend in some sense theorems of Muñoz Fernández et al. [Linear Algebra Appl. 428 (2008)].

Authors

  • Giuseppina BarbieriDipartimento di Matematica e Informatica
    Università di Udine
    33100 Udine, Italy
    e-mail
  • Francisco J. García-PachecoDepartment of Mathematical Sciences
    University of Cadiz
    Puerto Real 11510, Spain
    e-mail
  • Daniele PuglisiDepartment of Mathematics and Computer Sciences
    University of Catania
    95125, Catania, Italy
    e-mail

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