@article { Gutman20070820,
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"
}
@inproceedings { Gutman20070920,
author = "Gutman A.E. and Koptev A.V.",
howpublished = "Electronic",
title = "The space of $CD_0$-sections of a Banach bundle",
booktitle = "Mathematics in the Modern World. The Russian Conference Dedicated to the 50th Anniversary of the Sobolev Institute of Mathematics (Novosibirsk, September 17--23, 2007): Proceedings",
address = "Novosibirsk",
publisher = "Sobolev Institute of Mathematics SB RAS",
year = "2007",
pages = "61--62",
language = "russian",
annote = "The space $CD_0(Q)=C(Q)+c_0(Q)$ introduced as an example of a Banach lattice with some unusual order-topological properties became the subject of further intensive study. One of the results of the study was the representation of $CD_0(Q)$ as the space $C(Q^{\bullet})$ of continuous functions on the set $Q^{\bullet}=Q\times\{0,1\}$ endowed with a special compact Hausdorff topology. In this paper, we extend the result to the case of sections of Banach bundles."
}
@article { Gutman20070926,
author = "Gutman A.E. and Koptev A.V.",
title = "Spaces of $CD_0$-functions and Alexandroff duplicate",
journal = "Vladikavk. Math. J.",
year = "2007",
volume = "9",
number = "3",
pages = "11--21",
language = "russian",
annote = "We first briefly expose some crucial phases in studying the space $CD_0(Q)=C(Q)+c_0(Q)$ whose elements are the sums of continuous and ``discrete'' functions defined on a compact Hausdorff space $Q$ without isolated points. In this part, special emphasis is on describing the compact space $Q^{\bullet}$ representing the Banach lattice $CD_0(Q)$ as $C(Q^{\bullet})$. In addition, a large fragment of the article is dedicated to the analogous frame related to the space $CD_0(Q,X)$ of ``continuous-discrete'' sections of a Banach bundle $X$ and the space of $CD_0$-homomorphisms of Banach bundles.",
keywords = "Banach lattice, AM-space, Alexandroff duplicate, continuous Banach bundle, section of a Banach bundle, Banach $C(Q)$-module, homomorphism of Banach bundles, homomorphism of $C(Q)$-modules"
}
@article { Gutman20081118,
author = "Gutman A.E. and Koptev A.V.",
howpublished = "Electronic",
title = "Spaces of $CD_0$-functions and $CD_0$-sections of Banach bundles",
journal = "Sib. Electron. Math. Rep.",
year = "2009",
volume = "6",
pages = "219--242",
annote = "We first briefly expose some crucial phases in studying the space $CD_0(Q)=C(Q)+c_0(Q)$ whose elements are the sums of continuous and ``discrete'' functions defined on a compact Hausdorff space $Q$ without isolated points. (In this part, special emphasis is on describing the compact space $Q^{\bullet}$ representing the Banach lattice $CD_0(Q)$ as $C(Q^{\bullet})$.) The rest of the article is dedicated to the analogous frame related to the space $CD_0(Q,X)$ of ``continuous-discrete'' sections of a Banach bundle $X$ and the space of $CD_0$-homomorphisms of Banach bundles.",
keywords = "Banach lattice, AM-space, Alexandroff duplicate, continuous Banach bundle, section of a Banach bundle, Banach $C(Q)$-module, homomorphism of Banach bundles, homomorphism of $C(Q)$-modules"
}
@article { Gutman20131119,
author = "Gutman A.E. and Koptev A.V.",
title = "Continuous-discrete sections of bundles of Banach lattices",
journal = "Vladikavk. Math. J.",
year = "2013",
volume = "15",
number = "4",
pages = "14--18",
doi = "10.23671/VNC.2013.4.7330",
language = "russian",
annote = "The notion of a continuous bundle of Banach lattices is clarified and the order properties are studied of the space of $CD_0$-sections of such a bundle.",
keywords = "continuous Banach bundle, Banach lattice, bundle of Banach lattices, $CD_0$-section of a Banach bundle, Alexandroff duplicate"
}