1Dipartimento di Matematica e Informatica Università di Udine 33100 Udine, Italy 2Department of Mathematical Sciences University of Cadiz Puerto Real 11510, Spain 3Department of Mathematics and Computer Sciences University of Catania 95125, Catania, Italy
Studia Mathematica, Tome 219 (2013) no. 2, pp. 155-161
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)].
Keywords:
proved infinite dimensional there exists infinite dimensional space x valued measures which have infinite variation sets positive lebesgue measure term spaceability shown mathcal lambda setminus sigma measures non sigma finite variation contains closed subspace other considerations concern space vector measures whose range neither closed nor convex those results extend sense theorems fern ndez linear algebra appl
Affiliations des auteurs :
Giuseppina Barbieri
1
;
Francisco J. García-Pacheco
2
;
Daniele Puglisi
3
1
Dipartimento di Matematica e Informatica Università di Udine 33100 Udine, Italy
2
Department of Mathematical Sciences University of Cadiz Puerto Real 11510, Spain
3
Department of Mathematics and Computer Sciences University of Catania 95125, Catania, Italy
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title = {Lineability and spaceability on vector-measure spaces},
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Giuseppina Barbieri; Francisco J. García-Pacheco; Daniele Puglisi. Lineability and spaceability on vector-measure spaces. Studia Mathematica, Tome 219 (2013) no. 2, pp. 155-161. doi: 10.4064/sm219-2-5
