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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2007, Volume 7, Issue 4, Pages 27–48 (Mi vngu271)  

This article is cited in 1 scientific paper (total in 1 paper)

Spaces of $CD_0$-sections and $CD_0$-homomorphisms of Banach bundles

A. E. Gutman, A. V. Koptev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: The Banach space $CD_0(Q,\mathcal{X})=C(Q,\mathcal{X})+c_0(Q,\mathcal{X})$ is considered whose elements are the sums of continuous and “discrete” sections of a Banach bundle $\mathcal{X}$ over a compact Hausdorff space $Q$ without isolated points. As is known, $CD_0(Q,\mathcal{X})$ is isometric to the space $C(\tilde{Q},\tilde{\mathcal{X}})$ of continuous sections of a Banach bundle $\tilde{\mathcal{X}}$ over the set $\tilde{Q}=Q\times\{0,1\}$ endowed with a special topology. The connections are clarified between $\mathcal{X}$ and $\tilde{\mathcal{X}}$ related to subbundles as well as to bundles obtained by a continuous change of variable and by the restriction onto a topological subspace. In addition, we introduce and study the space $CD_0[\mathcal{X},\mathcal{Y}]$ of $CD_0$-homomorphisms of Banach bundles $\mathcal{X}$ and $\mathcal{Y}$ and demonstrate that it possesses certain properties analogous to those of the space of $CD_0$-sections.

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UDC: 517.98
Received: 20.08.2007

Citation: A. E. Gutman, A. V. Koptev, “Spaces of $CD_0$-sections and $CD_0$-homomorphisms of Banach bundles”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 7:4 (2007), 27–48

Citation in format AMSBIB
\Bibitem{GutKop07}
\by A.~E.~Gutman, A.~V.~Koptev
\paper Spaces of $CD_0$-sections and $CD_0$-homomorphisms of Banach bundles
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2007
\vol 7
\issue 4
\pages 27--48
\mathnet{http://mi.mathnet.ru/vngu271}


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    This publication is cited in the following articles:
    1. A. E. Gutman, A. V. Koptev, “Nepreryvno-diskretnye secheniya rassloenii banakhovykh reshetok”, Vladikavk. matem. zhurn., 15:4 (2013), 14–18  mathnet
  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
    Number of views:
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