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The Rainwater–Simons weak convergence theorem for the Brown associated norm
A. R. Alimov^{} ^{} Faculty of Mechanics and Mathematics, Moscow State University, 119991 Moscow, Russia
Abstract:
The Rainwater–Simons weak convergence theorem is extended to the convergence with respect to the associated norm (in the sense of Brown), the latter proved useful, inter alia, in testing the membership of a point to the Banach–Mazur hull of two points, which is the intersection of all closed balls containing these points.
Keywords and phrases:
Rainwater–Simons convergence theorem, Brown associated norm, Menger connected set.
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MSC: 40A05 Received: 21.05.2014
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A. R. Alimov, “The Rainwater–Simons weak convergence theorem for the Brown associated norm”, Eurasian Math. J., 5:2 (2014), 126–131
Citation in format AMSBIB
\Bibitem{Ali14}
\by A.~R.~Alimov
\paper The RainwaterSimons weak convergence theorem for the Brown associated norm
\jour Eurasian Math. J.
\yr 2014
\vol 5
\issue 2
\pages 126131
\mathnet{http://mi.mathnet.ru/emj159}
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http://mi.mathnet.ru/eng/emj159 http://mi.mathnet.ru/eng/emj/v5/i2/p126
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This publication is cited in the following articles:

A. R. Alimov, “On finitedimensional Banach spaces in which suns are connected”, Eurasian Math. J., 6:4 (2015), 7–18

J. Carlos Ferrando, J. Kakol, M. LopezPellicer, “On spaces $C^b(X)$ weakly $k$analytic”, Math. Nachr., 290:16 (2017), 2612–2618

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