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

title = "On the notion of the dual of a Banach bundle",

journal = "Matem. tr.",

year = "1999",

volume = "2",

number = "1",

pages = "8--71",

language = "russian",

annote = "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.",

keywords = "continuous Banach bundle, dual Banach bundle, duality, homomorphism of Banach bundles, continuous section, weakly continuous section"

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

title = "On the notion of the dual of a Banach bundle",

journal = "Siberian Adv. Math.",

year = "1999",

volume = "9",

number = "1",

pages = "46--98",

annote = "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.",

keywords = "continuous Banach bundle, dual Banach bundle, duality, homomorphism of Banach bundles, continuous section, weakly continuous section"

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

chapter = "3",

title = "Dual Banach bundles",

booktitle = "Nonstandard analysis and vector lattices",

address = "Novosibirsk",

publisher = "Institute of Mathematics",

year = "1999",

pages = "127--202",

language = "russian",

annote = "The solution of the problem of defining and existence of a dual continuous Banach bundle (CBB) for the case of ample bundles over extremally disconnected compact spaces is essentially based on specific properties of ample bundles and extremally disconnected compact spaces and, thus, cannot be extended to a wider class of bundles. The natural intention to extend the domain of applications for the duality theory leads to the problem of constructing a dual CBB for an arbitrary Banach bundle over an arbitrary topological space. The study of this problem is the main subject of the present chapter, where, in particular, a definition of a dual bundle is presented, with the above-formulated requirements fulfilled, and a number of necessary and sufficient conditions is suggested for existence of a dual bundle."

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

chapter = "3",

title = "Dual Banach bundles",

booktitle = "Nonstandard analysis and vector lattices",

address = "Dordrecht",

publisher = "Kluwer Academic Publishers",

year = "2000",

pages = "105--159",

doi = "10.1007/978-94-011-4305-9_3",

annote = "The solution of the problem of defining and existence of a dual continuous Banach bundle (CBB) for the case of ample bundles over extremally disconnected compact spaces is essentially based on specific properties of ample bundles and extremally disconnected compact spaces and, thus, cannot be extended to a wider class of bundles. The natural intention to extend the domain of applications for the duality theory leads to the problem of constructing a dual CBB for an arbitrary Banach bundle over an arbitrary topological space. The study of this problem is the main subject of the present chapter, where, in particular, a definition of a dual bundle is presented, with the above-formulated requirements fulfilled, and a number of necessary and sufficient conditions is suggested for existence of a dual bundle."

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

title = "Finite representability in stalks of ample Banach bundles",

journal = "Vladikavk. Math. J.",

year = "2005",

volume = "7",

number = "1",

pages = "39--45",

language = "russian",

annote = "It is shown that the stalks of ample Banach bundles inherit (and strengthen in some cases) finite representability of a normed space in ``adjacent'' stalks. Each of the facts established in the paper can be regarded as an analog of the corresponding property of ultraproducts of Banach spaces.",

keywords = "local theory of Banach spaces, ultraproduct of Banach spaces, finite representability of a normed space, ample continuous Banach bundle"

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

chapter = "3",

title = "Dual Banach bundles",

booktitle = "Nonstandard analysis and vector lattices. 2nd ed., corr. and enl.",

address = "Novosibirsk",

publisher = "Institute of Mathematics",

year = "2005",

pages = "125--201",

language = "russian",

annote = "The solution of the problem of defining and existence of a dual continuous Banach bundle (CBB) for the case of ample bundles over extremally disconnected compact spaces is essentially based on specific properties of ample bundles and extremally disconnected compact spaces and, thus, cannot be extended to a wider class of bundles. The natural intention to extend the domain of applications for the duality theory leads to the problem of constructing a dual CBB for an arbitrary Banach bundle over an arbitrary topological space. The study of this problem is the main subject of the present chapter, where, in particular, a definition of a dual bundle is presented, with the above-formulated requirements fulfilled, and a number of necessary and sufficient conditions is suggested for existence of a dual bundle."

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

title = "Distribution of finite-dimensional and separable stalks of an ample Banach bundle",

journal = "Proc. Acad. Sci.",

year = "2014",

volume = "456",

number = "4",

pages = "387--388",

doi = "10.7868/S0869565214160038",

language = "russian",

annote = "The topological characteristics are studied of the set of points at which the stalks of an ample Banach bundle are finite-dimensional or separable. A connection is established between the property of the stalks of a bundle to be finite-dimensional or separable with the analogous property of the stalks of the ample hull of the bundle. A new criterion is obtained for existence of the dual bundle."

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

title = "Distribution of finite-dimensional and separable stalks of an ample Banach bundle",

journal = "Doklady Math.",

year = "2014",

volume = "89",

number = "3",

pages = "319--320",

doi = "10.1134/S1064562414030168",

annote = "The topological characteristics are studied of the set of points at which the stalks of an ample Banach bundle are finite-dimensional or separable. A connection is established between the property of the stalks of a bundle to be finite-dimensional or separable with the analogous property of the stalks of the ample hull of the bundle. A new criterion is obtained for existence of the dual bundle."

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

title = "Finite dimensionality and separability of the stalks of Banach bundles",

journal = "Sib. Matem. Zh.",

year = "2014",

volume = "55",

number = "2",

pages = "304--314",

language = "russian",

annote = "Topological characteristics are studied of the set of points at which the stalks of an ample Banach bundle over an extremally disconnected compact space are finite-dimensional or separable. A connection is established between finite dimensionality or separability of the stalks of a bundle and the analogous properties of the stalks of the ample hull of the bundle. A new criterion is obtained for existence of a dual bundle.",

keywords = "continuous Banach bundle, ample hull, extremally disconnected compact space, $\sigma$-isolated point"

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

title = "Finite dimensionality and separability of the stalks of Banach bundles",

journal = "Sib. Math. J.",

year = "2014",

volume = "55",

number = "2",

pages = "246--253",

doi = "10.1134/S0037446614020074",

annote = "Topological characteristics are studied of the set of points at which the stalks of an ample Banach bundle over an extremally disconnected compact space are finite-dimensional or separable. A connection is established between finite dimensionality or separability of the stalks of a bundle and the analogous properties of the stalks of the ample hull of the bundle. A new criterion is obtained for existence of a dual bundle.",

keywords = "continuous Banach bundle, ample hull, extremally disconnected compact space, $\sigma$-isolated point"

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

title = "Homomorphisms of Banach bundles and separated convergent sequences",

booktitle = "Geometry Days in Novosibirsk -- 2014. International conference dedicated to 85th anniversary of academician Yu.G.Reshetnyak (Novosibirsk, September 24--27, 2014): Proceedings",

address = "Novosibirsk",

publisher = "Sobolev Institute of Mathematics SB RAS",

year = "2014",

pages = "39--40",

language = "russian",

annote = "In the theory of continuous Banach bundles, the question remains open on existence of nonzero homomorphism in nonzero bundles. In this connection there is a need in general methods of constructing homomorphisms possessing certain approximating properties. The above topic covers the new facts presented here on existence of homomorphisms which assume prescribed values in the points of a convergent sequence."

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

title = "Lateral convergence and homomorphisms of Banach bundles",

journal = "Sib. Matem. Zh.",

year = "2025",

volume = "66",

number = "2",

pages = "188--203",

doi = "10.33048/smzh.2025.66.205",

language = "russian",

annote = "We introduce and study the concepts of injective and lateral convergence in a topological space and obtain some results on the existence of homomorphisms of continuous Banach bundles, as well as continuous and weakly continuous vector-valued functions and sections that take preassigned values at the points of injectively and laterally convergent sequences.",

keywords = "topological space, separation, convergent sequence, continuous Banach bundle, homomorphism, section"

author = "Gutman A.E. and Emelianenkov I.A.",

title = "Lateral convergence and homomorphisms of Banach bundles",

journal = "Sib. Math. J.",

year = "2025",

volume = "66",

number = "2",

pages = "279--290",

doi = "10.1134/S0037446625020053",

annote = "We introduce and study the concepts of injective and lateral convergence in a topological space and obtain some results on the existence of homomorphisms of continuous Banach bundles, as well as continuous and weakly continuous vector-valued functions and sections that take preassigned values at the points of injectively and laterally convergent sequences.",

keywords = "topological space, separation, convergent sequence, continuous Banach bundle, homomorphism, section"