Gutman A.E.
Bundles of Banach lattices
5 publications, 2000–2025

Development of the theory of continuous and measurable bundles of Banach lattices and the theory of Banach–Kantorovich lattices

The notions of continuous and measurable bundle of Banach lattices are introduced and studied.
Banach–Kantorovich lattices are represented as spaces of continuous sections of bundles of Banach lattices.
An analytic representation is obtained of the conditional expectation by means of stalkwise integration in a bundle of measure spaces.
It is shown that every positive lifting in a measurable bundle of Banach lattices is a lattice homomorphism.
Every monotone operator acting from a vector lattice to a normed space is represented as the composition of a lattice homomorphism and a linear isometry.
The previous result is extended to the case of an operator acting to a lattice-normed space.

1.	Gutman A.E., Kolesnikov A.S. Banach–Kantorovich lattices [in Russian]. Textbook. Novosibirsk: Novosib. State Univ., 2000. 80 p. Bibliographic record Record in BibTeX format Textbook (PDF) Cover (PDF) Information on ResearchGate
2.	Gutman A.E. Positive lifting in a measurable bundle of Banach lattices [in Russian] // Report abstract. Differential Equations. Function Spaces. Approximation Theory. International Conference dedicated to the 105th anniversary of the birthday of S.L.Sobolev (Novosibirsk, August 18–24, 2013): Proceeding. Novosibirsk: Institute of Mathematics SB RAS, 2013. P. 377. 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
3.	Gutman A.E. Positive lifting in a measurable bundle of Banach lattices [in Russian] // Vladikavk. Math. J. 2013. V. 15, issue 4. P. 12–13. 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
4.	Gutman A.E., Koptev A.V. Lattice-metric decomposition of a monotone operator [in Russian] // Math. Notes NEFU. 2013. V. 20, issue 2. P. 34–40. Bibliographic record Record in BibTeX format Article (PDF) Information on eLIBRARY Volume on the journal site Journal site
5.	Gutman A.E. Monotone operators in vector lattices and lattice-normed spaces // Sib. Math. J. 2025. V. 66, N 3. P. 826–831. Bibliographic record Record in BibTeX format Article (PDF) Information on Springer Link Information on ResearchGate DOI resolution Journal site

List in BibTeX format

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

Last updated
November 17, 2025

Gutman A.E.Bundles of Banach lattices5 publications, 2000–2025

Gutman A.E.
Bundles of Banach lattices
5 publications, 2000–2025