Order-bounded operators in vector lattices and in spaces of measurable functions

DOI10.1007/BF01322066zbMath0725.47033MaRDI QIDQ2276738

A. V. Bukhvalov

Publication date: 1991

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

zbMATH Keywords

spaces of measurable functionsdisjoint operatorsgeneralized Yosida-Hewitt theoremorder-bounded operators in vector latticesp- absolutely summing operators

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Positive linear operators and order-bounded operators (47B65) Ordered topological linear spaces, vector lattices (46A40)

Related Items

\((p,q)\)-regular operators between Banach lattices

Cites Work

• Extended orthomorphisms on Archimedean Riesz spaces
• One class of Toeplitz operators connected with the divisibility of analytic functions
• Factorization by lattice homomorphisms
• On the isometries of certain function-spaces
• On products of Orlicz spaces
• Orthomorphisms and Boolean algebras of projections
• The space of extended orthomorphisms in a Riesz space
• The problem of smallness for operator blocks in \(L_ p\) spaces
• The order bidual of lattice ordered algebras
• A characterization of orthogonal transition kernels
• Ideal properties of regular operators beween Banach lattices
• The classification of injective Banach lattices
• Ideals and bands in principal modules
• A partial spectral reduction for positive linear operators
• One-parameter semigroups of positive operators
• A characterization of weakly sequentially complete Banach lattices
• The range of an operator in C(X) and its representing stochastic kernel
• Factorization of positive multilinear maps
• The modulus of a weakly compact operator
• Factorization of operators through \(L_{p\infty}\) or \(L_{p1}\) and non- commutative generalizations
• Order p-summing operators, p-stable distributions and characterizations of \(L^ p\)-spaces
• Extension of linear 0-continuous operators
• Interpolation of linear operators in spaces of vector-valued functions and with mixed norm
• An interpolation result for the spectral radius
• Hilbertian and complemented finite-dimensional subspaces of Banach lattices and unitary ideals
• Positive compact operators on Banach lattices
• Disjoint sequences, compactness, and semireflexivity in locally convex Riesz spaces
• A factorization theorem in Banach lattices and its application to Lorentz spaces
• Compact operators in Banach lattices
• Summing and serially summing operators and characterization of AL-spaces
• Compactness properties of abstract kernel operators
• A characterization of non-Dunford-Pettis operators on \(L^ 1\).
• On the 0-spektrum of regular operators and the spectrum of measures
• Isomorphisms between \(L_ p\)-function spaces when \(p<1\)
• On lattice properties of the composition operator
• Extension of positive operators and Korovkin theorems
• On permanence properties of sublinear operators
• The Banach-Saks property is not \(L^ 2\)-hereditary
• Injective Banach lattices with strong order units
• Unital embedding and complexifications of F-algebras
• General principle of local reflexivity in the theory of cone duality
• The components of a positive operator
• Absolutely summing operators and local unconditional structures
• Über Klassen schwach kompakter Operatoren in Banachverbänden
• The structure space of a Banach lattice
• Eine Bemerkung über Tensorprodukte von Banachverbänden
• On Banach lattices of operators
• Disjunkte Folgen in Banachverbänden und Kegel-absolutsummierende Operatoren
• Lattice isomorphisms of the spaces \(W^1_n\) and quasiconformal mappings
• Sur les opérateurs linéaires qui transforment la boule unite d'un espace de Banach en une partie latticiellement bornee d'un espace de Banach reticule
• Operator algebras and invariant subspaces
• Injective Banach lattices
• Richesses du centre d'un espace vectoriel reticule
• Operators with absolutely bounded matrices
• Über approximativ faktorisierbare Operatoren
• Groupes et anneaux reticules
• Conditional expectation and ordering
• Représentations d'opérateurs à valeurs dans \(L^1(X,\Sigma,\mu)\)
• Embedding \(L_1\) in a Banach lattice
• Schrödinger operators with magnetic fields. I: General interactions
• Eine Variante des Rieszschen Darstellungssatzes und ein Zerlegungssatz für sublineare Operatoren
• Characterization and order properties of pseudo-integral operators
• Über den Absolutbetrag auf komplexen Vektorverbänden
• Some characterizations of AM- and AL-spaces
• On factorization of Orlicz spaces
• Tensor products of Banach lattices
• Contractive projections on an \(L_ 1\) space
• Banachverbände und positive Projektionen
• Isometries of certain function spaces
• On the isometries of reflexive Orlicz spaces
• Contractive projections in \(L_ p\)-spaces
• On two classes of linear mappings, acting between Banach spaces and Banach lattices
• Complete continuity of integral operators
• The ring of polar preserving endomorphisms of an abelian lattice-ordered group
• A note on the characterization of conditional expectation operators
• The ideal center of partially ordered vector spaces
• Banach lattices of compact maps
• Integraldarstellung regulärer Operatoren auf Banachverbänden. (Integral representation of regular operators on Banach lattices)
• Kompaktheit von Integraloperatoren auf Banachverbänden
• Normed tensor products of Banach lattices
• Order-theoretic characterization of Hilbert-Schmidt operators
• Sur quelques notions fondamentales dans la théorie générale des opérations linéaires
• Schrödinger semigroups
• On p-absolutely summing operators acting on Banach lattices
• Operators which Factor through Convex Banach Lattices
• Subsequence principles for vector-valued random variables
• On Order Properties of Order Bounded Transformations
• Extension of Vector Lattice Homomorphisms
• A Noncompletely Continuous Operator on L 1 (G) whose Random Fourier Transform is in c 0 (G)
• The ideal property of tensor products of Banach lattices with applications to the local structure of spaces of absolutely summing operators
• Compactness Properties of An Operator which Imply that It is an Integral Operator
• A Note on Disjointness Preserving Operators
• Application of methods of the theory of order-bounded operators to the theory of operators inL^p-spaces
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• CHOQUET BOUNDARIES INK-SPACES
• A Lattice Theoretic Characterization of an Integral Operator
• Cones in the Tensor Product of Locally Convex Lattices
• Riesz spaces with the order-continuity property. I
• Extensions and Liftings of Positive Linear Mappings on Banach Lattices
• Ergodic Properties of Lamperti Operators
• Riesz spaces with the order-continuity property. II
• SUBLINEAR OPERATORS AND THEIR APPLICATIONS
• Perturbation of Translation Invariant Positivity Preserving Semigroups on L 2 (R N )
• Approximation by Weakly Compact Operators inL1
• A note on diffuse random measures
• Order bounded operators and tensor products of Banach lattices.
• Preregular maps between Banach lattices
• FUNCTORS IN CATEGORIES OF BANACH SPACES
• Remark on the modulus of compact operators
• A generalization of a problem of Steinhaus
• The homotopy structure of the linear group of a Banach space
• Tensor Products of Archimedean Vector Lattices
• A note on the lattice properties of the linear maps of finite rank
• An Example in the Space of Bounded Operators from C(X) to C(Y)
• Produits tensoriels topologiques et espaces nucléaires
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Lattice Analogues of Absolutely Summing Constants^*
• On Lattice Summing Operators
• Convexity conditions for non-locally convex lattices
• Operators on Banach Lattices as Weighted Compositions
• The order boundedness of band preserving operators on uniformly complete vector lattices
• RELATIVELY CENTRAL OPERATORS ON ARCHIMEDEAN VECTOR LATTICES—III
• Decompositions of vector measures in Riesz spaces and Banach lattices
• Isometries of L 1 ∩L p
• Maximal-Valued Extensions of Positive Operators
• Reflexivity and Order Properties of Scalar-Type Spectral Operators in Locally Convex Spaces
• p-Lattice Summing Operators
• On the Representation of Order Continuous Operators by Random Measures
• Compactness Properties of Carleman and Hille-Tamarkin Operators
• Isometries on L p,1
• Ideale regulärer Operatoren und Kompaktheit positiver Operatoren zwischen Banachverbänden
• Operators on Banach Lattices and the Radon-Nikodym Theorem
• Linear Operators in Banach Lattices and WeightedL2 Inequalities
• Lattice Properties of Integral Operators
• Pseudo-Integral Operators
• Banach Lattices of Bounded Operators
• BANACH LATTICES - SOME BANACH ASPECTS OF THEIR THEORY
• EXTREMAL STRUCTURE OF CONES OF OPERATORS
• Extensions of positive operators and extreme points. I
• Extensions of positive operators and extreme points. II
• Extensions of positive operators and extreme points. III
• Extensions of positive operators and extreme points. IV
• Extension of Vector-Lattice Homomorphisms
• A CHARACTERIZATION OF THE BAND OF KERNEL OPERATORS
• Orthomorphisms of archimedean vector lattices
• Almost Compactness and Decomposability of Integral Operators
• A New Proof of the Lattice Structure of Orthomorphisms
• Radon-Nikodym Derivatives for Banach Lattice-Valued Measures
• The order dual of an abelian von Neumann algebra
• Lattice bounding, Radonifying and summing mappings
• A Direct Proof of the Matthes-Wright Integral Extension Theorem
• Extensions of positive operators between Banach lattices
• Applications of Banach ideals of operators