Compactness in L¹ of a vector measure

J. M. Calabuig, et al. "Compactness in L¹ of a vector measure." Studia Mathematica 225.3 (2014): 259-282. <http://eudml.org/doc/286575>.

@article{J2014,
abstract = {We study compactness and related topological properties in the space L¹(m) of a Banach space valued measure m when the natural topologies associated to convergence of vector valued integrals are considered. The resulting topological spaces are shown to be angelic and the relationship of compactness and equi-integrability is explored. A natural norming subset of the dual unit ball of L¹(m) appears in our discussion and we study when it is a boundary. The (almost) complete continuity of the integration operator is analyzed in relation with the positive Schur property of L¹(m). The strong weakly compact generation of L¹(m) is discussed as well.},
author = {J. M. Calabuig, S. Lajara, J. Rodríguez, E. A. Sánchez-Pérez},
journal = {Studia Mathematica},
keywords = {vector measure; integration operator; compactness; angelic space; boundary; positive Schur property; completely continuous operator; almost Dunford-Pettis operator; strongly weakly compactly generated space},
language = {eng},
number = {3},
pages = {259-282},
title = {Compactness in L¹ of a vector measure},
url = {http://eudml.org/doc/286575},
volume = {225},
year = {2014},
}

TY - JOUR
AU - J. M. Calabuig
AU - S. Lajara
AU - J. Rodríguez
AU - E. A. Sánchez-Pérez
TI - Compactness in L¹ of a vector measure
JO - Studia Mathematica
PY - 2014
VL - 225
IS - 3
SP - 259
EP - 282
AB - We study compactness and related topological properties in the space L¹(m) of a Banach space valued measure m when the natural topologies associated to convergence of vector valued integrals are considered. The resulting topological spaces are shown to be angelic and the relationship of compactness and equi-integrability is explored. A natural norming subset of the dual unit ball of L¹(m) appears in our discussion and we study when it is a boundary. The (almost) complete continuity of the integration operator is analyzed in relation with the positive Schur property of L¹(m). The strong weakly compact generation of L¹(m) is discussed as well.
LA - eng
KW - vector measure; integration operator; compactness; angelic space; boundary; positive Schur property; completely continuous operator; almost Dunford-Pettis operator; strongly weakly compactly generated space
UR - http://eudml.org/doc/286575
ER -