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This article is cited in 2 scientific papers (total in 2 papers)
The Banach–Steinhaus Uniform Boundedness Principle for Operators in Banach–Kantorovich Spaces over $L^0$
I. G. Ganieva, K. K. Kudaibergenovb a Tashkent Temir YO'L Muxandislari Instituti
b Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan
Abstract:
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.
Key words:
Banach–Kantorovich space, measurable Banach bundle, vector-valued lifting, cyclically compact set.
Received: 07.12.2004
Citation:
I. G. Ganiev, K. K. Kudaibergenov, “The Banach–Steinhaus Uniform Boundedness Principle for Operators in Banach–Kantorovich Spaces over $L^0$”, Mat. Tr., 9:1 (2006), 21–33; Siberian Adv. Math., 16:3 (2006), 42–53
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https://www.mathnet.ru/eng/mt37 https://www.mathnet.ru/eng/mt/v9/i1/p21
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