Lineability and spaceability on vector-measure spaces

Giuseppina Barbieri, Francisco J. García-Pacheco, and Daniele Puglisi. "Lineability and spaceability on vector-measure spaces." Studia Mathematica 219.2 (2013): 155-161. <http://eudml.org/doc/285790>.

@article{GiuseppinaBarbieri2013,
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 $ca(ℬ,λ,X)∖ M_\{σ\}$, the measures with non-σ-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)].},
author = {Giuseppina Barbieri, Francisco J. García-Pacheco, Daniele Puglisi},
journal = {Studia Mathematica},
keywords = {lineability; spaceability; Banach space-valued vector meaures},
language = {eng},
number = {2},
pages = {155-161},
title = {Lineability and spaceability on vector-measure spaces},
url = {http://eudml.org/doc/285790},
volume = {219},
year = {2013},
}

TY - JOUR
AU - Giuseppina Barbieri
AU - Francisco J. García-Pacheco
AU - Daniele Puglisi
TI - Lineability and spaceability on vector-measure spaces
JO - Studia Mathematica
PY - 2013
VL - 219
IS - 2
SP - 155
EP - 161
AB - 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 $ca(ℬ,λ,X)∖ M_{σ}$, the measures with non-σ-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)].
LA - eng
KW - lineability; spaceability; Banach space-valued vector meaures
UR - http://eudml.org/doc/285790
ER -