Gutman A.E.
Order analysis
20 publications, 1988–2004

Development of the theory of lattice-normed spaces and dominated operators

The concept is developed of order approximation in lattice-normed spaces.
Four types of order boundedness of an operator are introduced and studied, examples are presented which demonstrate that the types are different.
Lattice-normed spaces are represented as spaces of extended continuous sections of ample Banach bundles.
The decomposition is obtained of an arbitrary order-bounded disjointness preserving operator into a strongly disjoint sum of weighted shift operators.
Function representations are obtained for a wide class of disjointness preserving operators, their properties are interpreted in terms of the representation.
The bands are studied which are generated by disjointness preserving operators in lattice-normed spaces.

1.	Gutman A.E. Multiplicative representation of disjointness preserving operators [in Russian]. Diploma thesis. Dept. of Math. Anal., Faculty of Mech. and Math., Novosib. State Univ., Novosibirsk, 1988. 94 p. Bibliographic record Record in BibTeX format Diploma thesis (PDF) Cover (PDF) Information on ResearchGate DOI resolution
2.	Gutman A.E. On disjointness preserving operators in Banach–Kantorovich spaces [in Russian] // Report abstract. XIV School on the theory of operators in function spaces (Novgorod, September 6–14, 1989): Proceedings. Novgorod, 1989. Part 1. P. 75. Bibliographic record Record in BibTeX format Report abstract (PDF) Cover (PDF) Information on ResearchGate
3.	Gutman A.E. An example of a sequentially o-continuous but not dominated disjointness preserving operator [in Russian] // Optimization. 1990. Issue 47(64). P. 116–121. Bibliographic record Record in BibTeX format Article (PDF) Cover (PDF) Information on ResearchGate
4.	Gutman A.E. On disjointness preserving operators in spaces of continuous functions [in Russian] // Report abstract. XV All-USSR School on the theory of operators in function spaces (Ulyanovsk, September 5–12, 1990): Proceedings. Ulyanovsk, 1990. Part 1. P. 76. Bibliographic record Record in BibTeX format Report abstract (PDF) Cover (PDF) Information on ResearchGate
5.	Gutman A.E. Measurable Banach bundles and weight operators [in Russian] // Report abstract. The Fifth School of Siberian and Far-Eastern young mathematicians (Novosibirsk, December 10–16, 1990): Proceedings. Novosibirsk, 1990. P. 30–32. Bibliographic record Record in BibTeX format Report abstract (PDF) Cover (PDF) Information on ResearchGate
6.	Gutman A.E. On the representation of lattice-normed spaces [in Russian] // Sib. Matem. Zh. 1991. V. 32, N 2. P. 41–54. Bibliographic record Record in BibTeX format Article (PDF) Cover (PDF) Information on ResearchGate Journal site English version
	Gutman A.E. On the realization of lattice-normed spaces // Sib. Math. J. 1991. V. 32, N 2. P. 210–221. Bibliographic record Record in BibTeX format Article (PDF) Cover (PDF) Information on Springer Link Information on ResearchGate DOI resolution Journal site Russian version
7.	Gutman A.E. Representation of lattice-normed spaces and its applications [in Russian]. Diss. abstract ... Ph.D. in mathematics: 01.01.01. Sobolev Inst. Math., Novosibirsk, 1991. 14 p. Bibliographic record Record in BibTeX format Dissertation abstract (PDF) Dissertation Copy on the RSL site Information on ResearchGate DOI resolution
8.	Gutman A.E. Representation of lattice-normed spaces and its applications [in Russian]. Diss. ... Ph.D. in mathematics: 01.01.01. Sobolev Inst. Math., Novosibirsk, 1991. 110 p. Bibliographic record Record in BibTeX format Dissertation (PDF) Dissertation abstract Information on ResearchGate DOI resolution
9.	Gutman A.E. Lifting in the space of measurable sections [in Russian] // Report abstract. XV All-USSR School on the theory of operators in function spaces (Nizhny Novgorod, September 13–20, 1991): Proceedings. Nizhny Novgorod, 1991. P. 63. Bibliographic record Record in BibTeX format Report abstract (PDF) Cover (PDF) Information on ResearchGate
10.	Gutman A.E. Banach bundles in the theory of lattice-normed spaces. I. Continuous Banach bundles // Siberian Adv. Math. 1993. V. 3, N 3. P. 1–55. Bibliographic record Record in BibTeX format Article (PDF) Cover (PDF) Information on ResearchGate Journal site
11.	Gutman A.E. Banach bundles in the theory of lattice-normed spaces. II. Measurable Banach bundles // Siberian Adv. Math. 1993. V. 3, N 4. P. 8–40. Bibliographic record Record in BibTeX format Article (PDF) Cover (PDF) Information on ResearchGate Journal site
12.	Gutman A.E. Banach bundles in the theory of lattice-normed spaces. III. Approximating sets and bounded operators // Siberian Adv. Math. 1994. V. 4, N 2. P. 54–75. Bibliographic record Record in BibTeX format Article (PDF) Cover (PDF) Information on ResearchGate Journal site
13.	Gutman A.E. Banach bundles in the theory of lattice-normed spaces [in Russian] // Linear operators coordinated with order. Novosibirsk: IM SB RAS, 1995. / Proc. Inst. Math. SB RAS. V. 29. P. 63–211. Bibliographic record Record in BibTeX format Article (PDF) Cover (PDF) Article on the journal site (PDF) Information on ResearchGate Journal site
14.	Gutman A.E. Banach bundles in the theory of lattice-normed spaces [in Russian]. Diss. abstract ... D.Sc. in mathematics: 01.01.01. Sobolev Inst. Math., Novosibirsk, 1995. 16 p. Bibliographic record Record in BibTeX format Dissertation abstract (PDF) Cover (PDF) Dissertation Copy on the RSL site Information on ResearchGate DOI resolution
15.	Gutman A.E. Banach bundles in the theory of lattice-normed spaces [in Russian]. Diss. ... D.Sc. in mathematics: 01.01.01. Sobolev Inst. Math., Novosibirsk, 1995. 312 p. Bibliographic record Record in BibTeX format Dissertation (PDF) Smaller font version (PDF) Report presentation (PDF) Dissertation abstract Information on ResearchGate DOI resolution
16.	Gutman A.E. Banach bundles in the theory of lattice-normed spaces. IV. Disjointness preserving operators // Siberian Adv. Math. 1996. V. 6, N 2. P. 35–102. Bibliographic record Record in BibTeX format Article (PDF) Cover (PDF) Information on ResearchGate Journal site
17.	Bukhvalov A.V., Gutman A.E., Korotkov V.B., Kusraev A.G., Kutateladze S.S., Makarov B.M. Vector lattices and integral operators. Dordrecht: Kluwer, 1996. ix+462 p. Bibliographic record Record in BibTeX format Monograph (PDF) Cover (PDF) Information on the Springer site Information on ResearchGate DOI resolution Chapter 5
18.	Gutman A.E. Disjointness preserving operators // Chapter 5 in: Vector lattices and integral operators. Dordrecht: Kluwer, 1996. P. 360–454. Bibliographic record Record in BibTeX format Chapter (PDF) Cover (PDF) Information on Springer Link Information on ResearchGate DOI resolution The whole book
19.	Gutman A.E., Feofanov D.S. Analytic description of principal operator bands [in Russian]. Textbook. Novosibirsk: Novosib. State Univ., 2000. 31 p. Bibliographic record Record in BibTeX format Textbook (PDF) Cover (PDF) Information on ResearchGate
20.	Gutman A.E., Feofanov D.S. Description of principal bands generated by disjointness preserving operators [in Russian] // Vladikavk. Math. J. 2004. V. 6, issue 3. P. 26–35. 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

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Last updated
June 10, 2020

Gutman A.E.Order analysis20 publications, 1988–2004

Gutman A.E.
Order analysis
20 publications, 1988–2004