Vector Measures, c₀, and (sb) Operators

Elizabeth M. Bator, Paul W. Lewis, and Dawn R. Slavens. "Vector Measures, c₀, and (sb) Operators." Bulletin of the Polish Academy of Sciences. Mathematics 54.1 (2006): 63-73. <http://eudml.org/doc/280716>.

@article{ElizabethM2006,
abstract = {Emmanuele showed that if Σ is a σ-algebra of sets, X is a Banach space, and μ: Σ → X is countably additive with finite variation, then μ(Σ) is a Dunford-Pettis set. An extension of this theorem to the setting of bounded and finitely additive vector measures is established. A new characterization of strongly bounded operators on abstract continuous function spaces is given. This characterization motivates the study of the set of (sb) operators. This class of maps is used to extend results of P. Saab dealing with unconditionally converging operators. A characterization of the existence of a countably additive, non-strongly bounded representing measure in terms of c₀ is presented. This characterization resolves a question posed in 1970.},
author = {Elizabeth M. Bator, Paul W. Lewis, Dawn R. Slavens},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {vector measure; representing measure; strongly additive; strongly bounded; (sb) operator},
language = {eng},
number = {1},
pages = {63-73},
title = {Vector Measures, c₀, and (sb) Operators},
url = {http://eudml.org/doc/280716},
volume = {54},
year = {2006},
}

TY - JOUR
AU - Elizabeth M. Bator
AU - Paul W. Lewis
AU - Dawn R. Slavens
TI - Vector Measures, c₀, and (sb) Operators
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2006
VL - 54
IS - 1
SP - 63
EP - 73
AB - Emmanuele showed that if Σ is a σ-algebra of sets, X is a Banach space, and μ: Σ → X is countably additive with finite variation, then μ(Σ) is a Dunford-Pettis set. An extension of this theorem to the setting of bounded and finitely additive vector measures is established. A new characterization of strongly bounded operators on abstract continuous function spaces is given. This characterization motivates the study of the set of (sb) operators. This class of maps is used to extend results of P. Saab dealing with unconditionally converging operators. A characterization of the existence of a countably additive, non-strongly bounded representing measure in terms of c₀ is presented. This characterization resolves a question posed in 1970.
LA - eng
KW - vector measure; representing measure; strongly additive; strongly bounded; (sb) operator
UR - http://eudml.org/doc/280716
ER -