Gutman A.E. Banach bundles (9 publications, 1999

Gutman A.E.
Banach bundles
9 publications, 1999–2025

Development of the theory of continuous and measurable Banach bundles

The theory of ample continuous Banach bundles is created.
The theory of measurable Banach bundles is created.
The notion of lifting in the space of measurable sections is introduced, and the corresponding theory is created.
Banach bundles of operator spaces are defined and studied.
The notion of dual Banach bundle is introduced, and the corresponding duality is studied.
It is shown that the stalks of ample Banach bundles inherit finite representability of a normed space in “adjacent” stalks.
Topological properties are studied of the sets of points at which the stalks of an ample Banach bundle are finite-dimensional or separable.
The concepts of injective and lateral convergence in a topological space are introduced and studied.
The existence is established of homomorphisms and sections of continuous Banach bundles that take preassigned values at the points of injectively and laterally convergent sequences.

List in BibTeX format

The papers are presented here for academic purposes and are not intended for mass dissemination or copying.

Last updated
March 21, 2025

1.	Gutman A.E., Koptev A.V. On the notion of the dual of a Banach bundle [in Russian] // Matem. tr. 1999. V. 2, N 1. P. 8–71. Bibliographic record Record in BibTeX format Article (PDF) Abstract (PDF) Cover (PDF) Abstract on the journal site Information on ResearchGate Issue on the journal site Journal site English version
	Gutman A.E., Koptev A.V. On the notion of the dual of a Banach bundle // Siberian Adv. Math. 1999. V. 9, N 1. P. 46–98. Bibliographic record Record in BibTeX format Article (PDF) Cover (PDF) Information on ResearchGate Journal site Russian version
2.	Gutman A.E., Koptev A.V. Dual Banach bundles [in Russian] // Chapter 3 in: Nonstandard analysis and vector lattices. Novosibirsk: Institute of Mathematics, 1999. P. 127–202. Bibliographic record Record in BibTeX format Chapter (PDF) Cover (PDF) Information on ResearchGate The whole book Second edition English version
3.	Gutman A.E., Koptev A.V. Dual Banach bundles // Chapter 3 in: Nonstandard analysis and vector lattices. Dordrecht: Kluwer Academic Publishers, 2000. P. 105–159. Bibliographic record Record in BibTeX format Chapter (PDF) Cover (PDF) Information on Springer Link Information on ResearchGate DOI resolution The whole book Russian version
4.	Gutman A.E., Koptev A.V., Popov A.I. Finite representability in stalks of ample Banach bundles [in Russian] // Vladikavk. Math. J. 2005. V. 7, issue 1. P. 39–45. Bibliographic record Record in BibTeX format Article (PDF) Cover (PDF) Article on the journal site (PDF) Information on the journal site Information on ResearchGate Journal site
5.	Gutman A.E., Koptev A.V. Dual Banach bundles [in Russian] // Chapter 3 in: Nonstandard analysis and vector lattices. 2nd ed., corr. and enl. Novosibirsk: Institute of Mathematics, 2005. P. 125–201. Bibliographic record Record in BibTeX format Chapter (PDF) Cover (PDF) Information on ResearchGate The whole book First edition
6.	Gutman A.E., Koptev A.V. Distribution of finite-dimensional and separable stalks of an ample Banach bundle [in Russian] // Proc. Acad. Sci. 2014. V. 456, N 4. P. 387–388. Bibliographic record Record in BibTeX format Article (PDF) Information on eLIBRARY Information on ResearchGate DOI resolution Journal site English version
	Gutman A.E., Koptev A.V. Distribution of finite-dimensional and separable stalks of an ample Banach bundle // Doklady Math. 2014. V. 89, N 3. P. 319–320. Bibliographic record Record in BibTeX format Article (PDF) Information on Springer Link Information on ResearchGate DOI resolution Journal site Russian version
7.	Gutman A.E., Koptev A.V. Finite dimensionality and separability of the stalks of Banach bundles [in Russian] // Sib. Matem. Zh. 2014. V. 55, N 2. P. 304–314. Bibliographic record Record in BibTeX format Article (PDF) Cover (PDF) Article on the journal site (PDF) Information on the journal site Information on ResearchGate Journal site English version
	Gutman A.E., Koptev A.V. Finite dimensionality and separability of the stalks of Banach bundles // Sib. Math. J. 2014. V. 55, N 2. P. 246–253. Bibliographic record Record in BibTeX format Article (PDF) Cover (PDF) Information on Springer Link Information on ResearchGate DOI resolution Journal site Russian version
8.	Koptev A.V., Gutman A.E. Homomorphisms of Banach bundles and separated convergent sequences [in Russian] // Report abstract. Geometry Days in Novosibirsk – 2014. International conference dedicated to 85th anniversary of academician Yu.G.Reshetnyak (Novosibirsk, September 24–27, 2014): Proceedings. Novosibirsk: Sobolev Institute of Mathematics SB RAS, 2014. P. 39–40. Bibliographic record Record in BibTeX format Report abstract (PDF) Cover (PDF) Abstracts (PDF) Conference program (PDF) Information on ResearchGate Abstracts on the site (PDF) Program on the conference site (PDF) Conference site
9.	Gutman A.E., Koptev A.V. Lateral convergence and homomorphisms of Banach bundles [in Russian] // Sib. Matem. Zh. 2025. V. 66, N 2. P. 188–203. Bibliographic record Record in BibTeX format Article (PDF) Article on the journal site (PDF) Information on the journal site Information on ResearchGate DOI resolution Journal site English version
	Gutman A.E., Emelianenkov I.A. Lateral convergence and homomorphisms of Banach bundles // Sib. Math. J. 2025. V. 66, N 2. P. 279–290. Bibliographic record Record in BibTeX format Article (PDF) Information on Springer Link Information on ResearchGate DOI resolution Journal site Russian version

Gutman A.E.Banach bundles9 publications, 1999–2025

Gutman A.E.
Banach bundles
9 publications, 1999–2025