On the Representation of Order Continuous Operators by Random Measures

DOI10.2307/1999450zbMath0599.47042OpenAlexW4249571475MaRDI QIDQ3733579

Lutz W. Weis

Publication date: 1984

Full work available at URL: https://doi.org/10.2307/1999450

zbMATH Keywords

convergence in measuretransition kernelsDunford-Pettis operatorsvector-valued martingalesspace of measurable functionsRiesz homomorphismsbands in the lattice of all order-continuous operatorscontinuity with respect to convergence in measureEnflo operatorsmartingale representations of operators

Mathematics Subject Classification ID

Integral operators (45P05) Linear operators on function spaces (general) (47B38) Linear operators on ordered spaces (47B60) Random measures (60G57)

Related Items (14)

Orthogonally Additive Operators on Vector Lattices ⋮ Ergodic decompositions of Dirichlet forms under order isomorphisms ⋮ Representation theorems for regular operators ⋮ On order isomorphisms intertwining semigroups for Dirichlet forms ⋮ Decomposition and representation of regular operators ⋮ Diffuse and atomic components of a positive operator ⋮ Rademacher bounded families of operators on 𝐿₁ ⋮ Unnamed Item ⋮ The Kalton and Rosenthal type decomposition of operators in Köthe-Bochner spaces ⋮ Order-bounded operators in vector lattices and in spaces of measurable functions ⋮ Real interpolation of domains of sectorial operators on \(L_p\)-spaces ⋮ A note on diffuse random measures ⋮ Nearly Representable Operators ⋮ The range of an operator in C(X) and its representing stochastic kernel

Cites Work

• Orthogonal transition kernels
• A characterization of non-Dunford-Pettis operators on \(L^ 1\).
• A positive compact operator
• Operator algebras and invariant subspaces
• Représentations d'opérateurs à valeurs dans \(L^1(X,\Sigma,\mu)\)
• Embedding \(L_1\) in a Banach lattice
• Characterization and order properties of pseudo-integral operators
• Approximation theorems for Markov operators
• Measurable sets of measures
• Integraldarstellung regulärer Operatoren auf Banachverbänden. (Integral representation of regular operators on Banach lattices)
• Bases, lacunary sequences and complemented subspaces in the spaces $L_{p}$
• Pseudo-Integral Operators
• Subspaces of $L^{1}$ containing $L^{1}$
• The Oscillation of an Operator on L p
• Extensions and Liftings of Positive Linear Mappings on Banach Lattices
• Every L p Operator is an L 2 Operator
• A note on diffuse random measures
• Convolution of singular measures
• Linear Operations on Summable Functions
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