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Matematicheskie Trudy, 1999, Volume 2, Number 1, Pages 8–71 (Mi mt146)  

This article is cited in 2 scientific papers (total in 2 papers)

On the Notion of the Dual of a Banach Bundle

A. E. Gutmana, A. V. Koptevb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Full-text PDF (633 kB) Citations (2)
Abstract: For an arbitrary continuous Banach bundle over an arbitrary topological space, the notion of a dual bundle is introduced and studied. Various necessary and sufficient conditions are presented for existence of a dual bundle, duality relations are examined between a bundle and its dual, an embedding of a bundle into its second dual is constructed, the notion of a weakly continuous section is introduced and studied. The questions under consideration are treated in the general case as well as for concrete classes of bundles and topological spaces. The results obtained are supplied with examples that justify accuracy of the results.
Key words: continuous Banach bundle, dual Banach bundle, duality, homomorphism of Banach bundles, continuous section, weakly continuous section.
Received: 17.11.1998
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
Citation: A. E. Gutman, A. V. Koptev, “On the Notion of the Dual of a Banach Bundle”, Mat. Tr., 2:1 (1999), 8–71; Siberian Adv. Math., 9:1 (1999), 46–98
Citation in format AMSBIB
\Bibitem{GutKop99}
\by A.~E.~Gutman, A.~V.~Koptev
\paper On~the~Notion of the~Dual of a~Banach~Bundle
\jour Mat. Tr.
\yr 1999
\vol 2
\issue 1
\pages 8--71
\mathnet{http://mi.mathnet.ru/mt146}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1762620}
\zmath{https://zbmath.org/?q=an:0938.46055}
\transl
\jour Siberian Adv. Math.
\yr 1999
\vol 9
\issue 1
\pages 46--98
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Математические труды Siberian Advances in Mathematics
     
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