The Banach--Steinhaus Uniform Boundedness Principle for Operators in Banach--Kantorovich Spaces over~$L^0$
Matematičeskie trudy, Tome 9 (2006) no. 1, pp. 21-33
Voir la notice de l'article provenant de la source Math-Net.Ru
We consider a vector-valued version of the Banach–Steinhaus uniform boundedness principle for universally complete Banach–Kantorovich spaces over the ring of measurable functions. We prove that, if a family of bounded linear operators in a universally complete Banach–Kantorovich space is pointwise bounded, then it is uniformly bounded. We also present applications to weak convergence and weak boundedness in universally complete Banach–Kantorovich spaces.
@article{MT_2006_9_1_a1,
author = {I. G. Ganiev and K. K. Kudaibergenov},
title = {The {Banach--Steinhaus} {Uniform} {Boundedness} {Principle} for {Operators} in {Banach--Kantorovich} {Spaces} over~$L^0$},
journal = {Matemati\v{c}eskie trudy},
pages = {21--33},
publisher = {mathdoc},
volume = {9},
number = {1},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MT_2006_9_1_a1/}
}
TY - JOUR AU - I. G. Ganiev AU - K. K. Kudaibergenov TI - The Banach--Steinhaus Uniform Boundedness Principle for Operators in Banach--Kantorovich Spaces over~$L^0$ JO - Matematičeskie trudy PY - 2006 SP - 21 EP - 33 VL - 9 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MT_2006_9_1_a1/ LA - ru ID - MT_2006_9_1_a1 ER -
%0 Journal Article %A I. G. Ganiev %A K. K. Kudaibergenov %T The Banach--Steinhaus Uniform Boundedness Principle for Operators in Banach--Kantorovich Spaces over~$L^0$ %J Matematičeskie trudy %D 2006 %P 21-33 %V 9 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/MT_2006_9_1_a1/ %G ru %F MT_2006_9_1_a1
I. G. Ganiev; K. K. Kudaibergenov. The Banach--Steinhaus Uniform Boundedness Principle for Operators in Banach--Kantorovich Spaces over~$L^0$. Matematičeskie trudy, Tome 9 (2006) no. 1, pp. 21-33. http://geodesic.mathdoc.fr/item/MT_2006_9_1_a1/