This article is cited in 2 papers

The Banach–Steinhaus Uniform Boundedness Principle for Operators in Banach–Kantorovich Spaces over $L^0$

I. G. Ganiev^a, K. K. Kudaibergenov<sup>b

a</sup> 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.

UDC: 517.98

Received: 07.12.2004

 English version: Siberian Advances in Mathematics, 2006, 16:3, 42–53

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