Compactness of the integration operator associated with a vector measure

S. Okada, W. J. Ricker, and L. Rodríguez-Piazza. "Compactness of the integration operator associated with a vector measure." Studia Mathematica 150.2 (2002): 133-149. <http://eudml.org/doc/285203>.

@article{S2002,
abstract = {A characterization is given of those Banach-space-valued vector measures m with finite variation whose associated integration operator Iₘ: f ↦ ∫fdm is compact as a linear map from L¹(m) into the Banach space. Moreover, in every infinite-dimensional Banach space there exist nontrivial vector measures m (with finite variation) such that Iₘ is compact, and other m (still with finite variation) such that Iₘ is not compact. If m has infinite variation, then Iₘ is never compact.},
author = {S. Okada, W. J. Ricker, L. Rodríguez-Piazza},
journal = {Studia Mathematica},
keywords = {vector measure; variation; integration operator; compact operator},
language = {eng},
number = {2},
pages = {133-149},
title = {Compactness of the integration operator associated with a vector measure},
url = {http://eudml.org/doc/285203},
volume = {150},
year = {2002},
}

TY - JOUR
AU - S. Okada
AU - W. J. Ricker
AU - L. Rodríguez-Piazza
TI - Compactness of the integration operator associated with a vector measure
JO - Studia Mathematica
PY - 2002
VL - 150
IS - 2
SP - 133
EP - 149
AB - A characterization is given of those Banach-space-valued vector measures m with finite variation whose associated integration operator Iₘ: f ↦ ∫fdm is compact as a linear map from L¹(m) into the Banach space. Moreover, in every infinite-dimensional Banach space there exist nontrivial vector measures m (with finite variation) such that Iₘ is compact, and other m (still with finite variation) such that Iₘ is not compact. If m has infinite variation, then Iₘ is never compact.
LA - eng
KW - vector measure; variation; integration operator; compact operator
UR - http://eudml.org/doc/285203
ER -