Lineability and spaceability on vector-measure spaces
Studia Mathematica, Tome 219 (2013) no. 2, pp. 155-161
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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
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author = {Giuseppina Barbieri and Francisco J. Garc{\'\i}a-Pacheco and Daniele Puglisi},
title = {Lineability and spaceability on vector-measure spaces},
journal = {Studia Mathematica},
pages = {155--161},
year = {2013},
volume = {219},
number = {2},
doi = {10.4064/sm219-2-5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm219-2-5/}
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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
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