author = "Gutman A.E. and Koptev A.V.",

title = "Spaces of $CD_0$-sections and $CD_0$-homomorphisms of Banach bundles",

journal = "Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.",

year = "2007",

volume = "7",

number = "4",

pages = "27--48",

language = "russian",

annote = "In the paper, the space $CD_0(Q,X)=C(Q,X)+c_0(Q,X)$ is considered whose elements are the sums of continuous and discrete sections of a Banach bundle $X$ over a compact Hausdorff space $Q$ without isolated points. As is known, this space is isometric to the space $C(Q^{\bullet},X^{\bullet})$ of continuous sections of some Banach bundle $X^{\bullet}$ over the compact space $Q^{\bullet}=Q\times\{0,1\}$ (with a special topology). We clarify the connection between $X$ and $X^{\bullet}$ on the example of subbundles as well as bundles obtained by continuous change of variables and by restriction onto a topological subspace. In addition, we introduce and study the space $CD_0[X,Y]$ of $CD_0$-homomorphisms of Banach bundles $X$ and $Y$ and show that is possesses some properties analogous to those of the space of $CD_0$-sections.",

keywords = "continuous Banach bundle, section of a Banach bundle, Banach $C(Q)$-module, homomorphism of Banach bundles, homomorphism of $C(Q)$-modules"