Geodesic
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

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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. 
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     author = {I. G. Ganiev and K. K. Kudaibergenov},
     title = {The {Banach--Steinhaus} {Uniform} {Boundedness} {Principle} for {Operators} in {Banach--Kantorovich} {Spaces} over~$L^0$},
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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/