Duality for unbounded order convergence and applications

DOI10.1007/s11117-017-0539-0zbMath1410.46010arXiv1705.06143OpenAlexW2615480476MaRDI QIDQ1670429

Niushan Gao, Denny H. Leung, Foivos Xanthos

Publication date: 5 September 2018

Published in: Positivity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.06143

zbMATH Keywords

monotonically complete Banach latticesorder continuous dualorder continuous predualrepresentation of convex functionalsunbounded order dual

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) Banach lattices (46B42) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Duality and reflexivity in normed linear and Banach spaces (46B10)

Related Items (21)

On unbounded order continuous operators ⋮ Automatic Fatou property of law-invariant risk measures ⋮ Completeness of unbounded convergences ⋮ A local Hahn-Banach theorem and its applications ⋮ Completeness for vector lattices ⋮ Unbounded topologies and \textit{uo}-convergence in locally solid vector lattices ⋮ The order-type Banach-Saks properties ⋮ Unbounded \(p\)-convergence in lattice-normed vector lattices ⋮ Weakly unbounded norm topology and \textit{wun}-Dunford-Pettis operators ⋮ On closedness of convex sets in Banach lattices ⋮ Free dual spaces and free Banach lattices ⋮ Embedded unbounded order convergent sequences in topologically convergent nets in vector lattices ⋮ Vector lattices with a Hausdorff uo-Lebesgue topology ⋮ \(um\)-topology in multi-normed vector lattices ⋮ \(u\tau \)-convergence in locally solid vector lattices ⋮ On closedness of law-invariant convex sets in rearrangement invariant spaces ⋮ Continuous functionals for unbounded convergence in Banach lattices ⋮ Неограниченные сходимости в конвергентных векторных решетках ⋮ Bibounded \(uo\)-convergence and \(b\)-property in vector lattices ⋮ Closedness of convex sets in Orlicz spaces with applications to dual representation of risk measures ⋮ Correction to: ``Unbounded order continuous operators on Riesz spaces.

Cites Work

• Functional analysis, Sobolev spaces and partial differential equations
• Banach lattices
• Fatou property, representations, and extensions of law-invariant risk measures on general Orlicz spaces
• Unbounded order convergence in dual spaces
• Unbounded order convergence and application to martingales without probability
• Uo-convergence and its applications to Cesàro means in Banach lattices
• Completeness of unbounded convergences
• On the C‐property and ‐representations of risk measures
• Biorthogonal systems in Banach spaces
• Stopping Times and Directed Processes
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