author = "Gutman A.E.",

school = "Dept. of Math. Anal., Faculty of Mech. and Math., Novosib. State Univ., Novosibirsk",

howpublished = "Manuscript",

title = "Multiplicative representation of disjointness preserving operators",

year = "1988",

pages = "94",

doi = "10.13140/RG.2.2.25057.61280",

language = "russian",

annote = "A diploma thesis in mathematics. Defended at the Department of Mathematical Analysis, Novosibirsk State University. Thesis adviser: Kusraev Anatoly Georgievich (D.Sc., Leading scientific officer at the Institute of Mathematics SB AS USSR)."

author = "Gutman A.E.",

title = "On disjointness preserving operators in Banach--Kantorovich spaces",

booktitle = "XIV School on the theory of operators in function spaces (Novgorod, September 6--14, 1989): Proceedings",

address = "Novgorod",

year = "1989",

volume = "1",

pages = "75",

language = "russian",

annote = "For a disjointness preserving linear operator acting from an arbitrary Banach--Kantorovich space in a universally complete Banach--Kantorovich space the equivalence is established of its $r$-$o$-continuity, $r$-continuity, majorizability, and multiplicativity on principal ideals."

author = "Gutman A.E.",

title = "An example of a sequentially $o$-continuous but not dominated disjointness preserving operator",

journal = "Optimization",

year = "1990",

volume = "47(64)",

pages = "116--121",

language = "russian",

annote = "An example is given of a linear operator acting from a Banach space into a Kantorovich space, which is sequentially $r$-continuous but not dominated."

author = "Gutman A.E.",

title = "On disjointness preserving operators in spaces of continuous functions",

booktitle = "XV All-USSR School on the theory of operators in function spaces (Ulyanovsk, September 5--12, 1990): Proceedings",

address = "Ulyanovsk",

year = "1990",

volume = "1",

pages = "76",

language = "russian",

annote = "For a disjointness preserving linear operator acting from a lattice-normed space of continuous vector-valued functions into a space of weakly continuous vector-valued functions the equivalence is established of its $r$-$o$-continuity, $r$-continuity, majorizability, and multiplicativity on principal ideals."

author = "Gutman A.E.",

title = "Measurable Banach bundles and weight operators",

booktitle = "The Fifth School of Siberian and Far-Eastern young mathematicians (Novosibirsk, December 10--16, 1990): Proceedings",

address = "Novosibirsk",

year = "1990",

pages = "30--32",

language = "russian",

annote = "The notion of measurable Banach bundle with lifting is introduced and studied. Representation is constructed of Banach--Kantorovich spaces and the corresponding homomorphisms by means of measurable sections of such bundles."

author = "Gutman A.E.",

title = "On the representation of lattice-normed spaces",

journal = "Sib. Matem. Zh.",

year = "1991",

volume = "32",

number = "2",

pages = "41--54",

language = "russian",

annote = "The concept is studied of complete (ample) Banach bundle and a representation is constructed of an arbitrary lattice-normed space as a space of maximal (extended) sections of such bundles. Criteria are also obtained for an operator in section spaces to admit a multiplicative representation that is a generalization of the composition of a change of variable and multiplication by a scalar-valued function (the so-called weighted shift)."

author = "Gutman A.E.",

title = "On the realization of lattice-normed spaces",

journal = "Sib. Math. J.",

year = "1991",

volume = "32",

number = "2",

pages = "210--221",

doi = "10.1007/BF00972767",

annote = "The concept is studied of complete (ample) Banach bundle and a representation is constructed of an arbitrary lattice-normed space as a space of maximal (extended) sections of such bundles. Criteria are also obtained for an operator in section spaces to admit a multiplicative representation that is a generalization of the composition of a change of variable and multiplication by a scalar-valued function (the so-called weighted shift)."

author = "Gutman A.E.",

school = "Sobolev Inst. Math., Novosibirsk",

type = "Dissertation abstract; Ph.D. in mathematics: 01.01.01",

howpublished = "Manuscript",

title = "Representation of lattice-normed spaces and its applications",

year = "1991",

pages = "14",

doi = "10.13140/RG.2.2.29671.34725",

language = "russian",

annote = "Abstract of a Dissertation for a degree of Ph.D. in mathematics, speciality 01.01.01: mathematical analysis. The dissertation is prepared at the Department of Analysis and Geometry of the Institute of Mathematics SB AS USSR. Scientific adviser: D.Sc. A.G.Kusraev. Official opponents: D.Sc., professor A.A.Tolstonogov, Ph.D., associate professor I.A.Shvedov. Lead organization: Leningrad State University. The presentation happened on June 19, 1991 within a session of Speciality Council K 002.23.02 at the Institute of Mathematics SB AS USSR, address: Universitetskij ave., 4, Novosibirsk, 630090. The abstract distributed on May 16, 1991. Academic secretary of the council: Ph.D. V.V.Ivanov."

author = "Gutman A.E.",

school = "Sobolev Inst. Math., Novosibirsk",

type = "Dissertation; Ph.D. in mathematics: 01.01.01",

howpublished = "Manuscript",

title = "Representation of lattice-normed spaces and its applications",

year = "1991",

pages = "110",

doi = "10.13140/RG.2.2.24218.75205",

language = "russian",

annote = "Dissertation for a degree of Ph.D. in mathematics, speciality 01.01.01: mathematical analysis. The dissertation is prepared at the Department of Analysis and Geometry of the Institute of Mathematics SB AS USSR. Scientific adviser: D.Sc. A.G.Kusraev. Official opponents: D.Sc., professor A.A.Tolstonogov, Ph.D., associate professor I.A.Shvedov. Lead organization: Leningrad State University. The presentation happened on June 19, 1991 within a session of Speciality Council K 002.23.02 at the Institute of Mathematics SB AS USSR, address: Universitetskij ave., 4, Novosibirsk, 630090. Academic secretary of the council: Ph.D. V.V.Ivanov."

author = "Gutman A.E.",

title = "Lifting in the space of measurable sections",

booktitle = "XV All-USSR School on the theory of operators in function spaces (Nizhny Novgorod, September 13--20, 1991): Proceedings",

address = "Nizhny Novgorod",

year = "1991",

pages = "63",

language = "russian",

annote = "It is shown that the space of classes of essentially bounded measurable functions acting into a Banach space $X$ admits a lifting if and only if the space $X$ is finitely-dimensional or the domain of definition is atomic. The minimal extension of a constant measurable Banach bundle is described which ensures existence of a lifting."

author = "Gutman A.E.",

title = "Banach bundles in the theory of lattice-normed spaces. I. Continuous Banach bundles",

journal = "Siberian Adv. Math.",

year = "1993",

volume = "3",

number = "3",

pages = "1--55",

annote = "Continuous Banach bundles over extremally disconnected compacta are considered. The notion of complete (ample) Banach bundle is introduced and discussed. The question is studied on representing lattice-normed spaces as spaces of continuous sections of Banach bundles.",

keywords = "extremally disconnected compactum, vector lattice, lattice-normed space, continuous Banach bundle, continuous vector-functions"

author = "Gutman A.E.",

title = "Banach bundles in the theory of lattice-normed spaces. II. Measurable Banach bundles",

journal = "Siberian Adv. Math.",

year = "1993",

volume = "3",

number = "4",

pages = "8--40",

annote = "The notions of measurable Banach bundle and lifting in a quotient space of measurable sections are introduced and discussed. The question is studied of representing lattice-normed spaces as those of measurable sections of Banach bundles.",

keywords = "measure space, extremally disconnected compactum, lifting, vector lattice, lattice-normed space, continuous and measurable Banach bundle"

author = "Gutman A.E.",

title = "Banach bundles in the theory of lattice-normed spaces. III. Approximating sets and bounded operators",

journal = "Siberian Adv. Math.",

year = "1994",

volume = "4",

number = "2",

pages = "54--75",

annote = "Two questions in the general theory of lattice-normed spaces (LNSs) are considered. First, the situation is studied when a subset of an LNS is order dense in the entire LNS; the notion of order approximation is introduced and described from various points of view. Second, the situation is studied when a linear operator from one LNS to another is order bounded; several different types of boundedness are introduced and studied in detail.",

keywords = "vector lattice, lattice-normed space, order approximating set, order bounded linear operator"

author = "Gutman A.E.",

title = "Banach bundles in the theory of lattice-normed spaces",

booktitle = "Linear operators coordinated with order",

address = "Novosibirsk",

publisher = "IM SB RAS",

journal = "Proc. Inst. Math. SB RAS",

year = "1995",

volume = "29",

pages = "63--211",

language = "russian",

annote = "The material is divided into six chapters, each of which consists of several sections. Chapter 1 contains definitions and preliminary information on the basic objects in use. The majority of sections of Chapter 2 can also be regarded preliminary, they include general information on continuous Banach bundles. Chapter 3 is central both in position and content: it concentrates the material related to ample Banach bundles and representation of lattice-normed spaces as spaces of sections. In Chapter 4, the theory of measurable Banach bundles is developed, which is made by transferring Daniell's scheme to the case of sections. In the same chapter, the notion of lifting in the space of measurable sections is introduced and studied, and the results are presented of applying the theory of ample Banach bundles to the study of measurable bundles. Chapter 5 contains applications of the results of the preceding chapters to various spaces of continuous and measurable vector-valued functions. Finally, Chapter 6 is devoted to the study of disjointness preserving operators and constructing analytic representations of such operators."

author = "Gutman A.E.",

school = "Sobolev Inst. Math., Novosibirsk",

type = "Dissertation abstract; D.Sc. in mathematics: 01.01.01",

howpublished = "Manuscript",

title = "Banach bundles in the theory of lattice-normed spaces",

year = "1995",

pages = "16",

doi = "10.13140/RG.2.2.30929.63842",

language = "russian",

annote = "Abstract of a Dissertation for a degree of D.Sc in mathematics, speciality 01.01.01: mathematical analysis. The dissertation is prepared at the Sobolev Institute of Mathematics SB RAS. Official opponents: D.Sc., professor A.V.Bukhvalov, D.Sc., professor S.K.Vodopyanov, D.Sc., professor S.P.Gulko. Lead organization: Nizhny Novgorod State University. The presentation happened on September 28, 1995 within a session of Dissertation Council D 002.23.02 for degrees of D.Sc in mathematics at the Sobolev Institute of Mathematics SB RAS, address: Universitetskij ave., 4, Novosibirsk, 630090. The abstract distributed on August 21, 1995. Academic secretary of the Dissertation Council: D.Sc. V.A.Sharafutdinov."

author = "Gutman A.E.",

school = "Sobolev Inst. Math., Novosibirsk",

type = "Dissertation; D.Sc. in mathematics: 01.01.01",

howpublished = "Manuscript",

title = "Banach bundles in the theory of lattice-normed spaces",

year = "1995",

pages = "312",

doi = "10.13140/RG.2.2.31670.19522",

language = "russian",

annote = "Dissertation for a degree of D.Sc in mathematics, speciality 01.01.01: mathematical analysis. The dissertation is prepared at the Sobolev Institute of Mathematics SB RAS. Official opponents: D.Sc., professor A.V.Bukhvalov, D.Sc., professor S.K.Vodopyanov, D.Sc., professor S.P.Gulko. Lead organization: Nizhny Novgorod State University. The presentation happened on September 28, 1995 within a session of Dissertation Council D 002.23.02 for degrees of D.Sc in mathematics at the Sobolev Institute of Mathematics SB RAS, address: Universitetskij ave., 4, Novosibirsk, 630090. Academic secretary of the Dissertation Council: D.Sc. V.A.Sharafutdinov."

author = "Gutman A.E.",

title = "Banach bundles in the theory of lattice-normed spaces. IV. Disjointness preserving operators",

journal = "Siberian Adv. Math.",

year = "1996",

volume = "6",

number = "2",

pages = "35--102",

annote = "In the present article, we study disjointness preserving operators that act in K-spaces and lattice-normed spaces. In particular, we find their analytic representations and decompositions into simpler components. We study orthomorphisms, shift operators, weighted shift operators, and arbitrary disjointness preserving operators.",

keywords = "vector lattice, lattice-normed space, continuous Banach bundle, continuous section, orthomorphism, shift operator, weighted shift operator, disjointness preserving operator, analytic representation"

author = "Bukhvalov A.V. and Gutman A.E. and Korotkov V.B. and Kusraev A.G. and Kutateladze S.S. and Makarov B.M.",

title = "Vector lattices and integral operators",

address = "Dordrecht",

publisher = "Kluwer",

year = "1996",

pages = "ix+462",

isbn = "978-94-010-6571-9",

doi = "10.1007/978-94-009-0195-7",

annote = "This volume is devoted to modern accomplishments in the field of vector lattices and integral operators which were achieved in Russia during the last two decades. Nonstandard methods are eleborated for the analysis of vector lattices and positive operators. Much attention is paid to studying stability under multiplication by an arbitrary bounded operator for various classes of operators which are defined in terms of order. Also, several approaches are treated to the solution of the J. von Neumann problem on the conditions for integrality of a linear operator, and full information is given on the solution of some problems posed by P.Halmos and V.Sunder. This book is intended for mathematicians, students and postgraduates interested in functional analysis, operator theory, geometry of Banach spaces and vector lattices."

author = "Gutman A.E.",

chapter = "5",

title = "Disjointness preserving operators",

booktitle = "Vector lattices and integral operators",

address = "Dordrecht",

publisher = "Kluwer",

year = "1996",

pages = "360--454",

doi = "10.1007/978-94-009-0195-7_5",

annote = "In this chapter, we study disjointness preserving operators in K-spaces and lattice-normed spaces. In particular, we find their analytic representations and decompositions into simpler components. We begin with studying general properties of disjointness preserving operators; then we consider orthomorphisms, shift operators, weighted shift operators, and, finally, return to arbitrary operators and apply the accumulated experience."

author = "Gutman A.E. and Feofanov D.S.",

note = "Textbook",

title = "Analytic description of principal operator bands",

address = "Novosibirsk",

publisher = "Novosib. State Univ.",

year = "2000",

pages = "31",

language = "russian",

annote = "In the paper, principal bands are studied in the spaces of operators acting in vector lattices and lattice-normed spaces. The key attention is paid to the bands generated by disjointness preserving operators. The main results are criteria for an operator to belong to the band generated by an operator in question. Every criterion provides a special analytic representation of the band under consideration."

author = "Gutman A.E. and Feofanov D.S.",

title = "Description of principal bands generated by disjointness preserving operators",

journal = "Vladikavk. Math. J.",

year = "2004",

volume = "6",

number = "3",

pages = "26--35",

language = "russian",

annote = "In the paper, principal bands are studied in the spaces of operators acting in vector lattices and lattice-normed spaces. The key attention is paid to the bands generated by disjointness preserving operators. The main results are criteria for an operator to belong to the band generated by an operator in question. Every criterion provides a special analytic representation of the band under consideration."