\(um\)-topology in multi-normed vector lattices

DOI10.1007/S11117-017-0533-6zbMath1398.46005arXiv1706.05755OpenAlexW2700629730MaRDI QIDQ1753002

M. A. A. Marabeh, Y. A. Dabboorasad, Eduard Yu. Emel'yanov

Publication date: 25 May 2018

Published in: Positivity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.05755

zbMATH Keywords

\(um\)-convergence\(um\)-topologymulti-normed vector lattice

Mathematics Subject Classification ID

Banach lattices (46B42) Ordered topological linear spaces, vector lattices (46A40)

Related Items (13)

\(o\tau \)-continuous, Lebesgue, KB, and Levi operators between vector lattices and topological vector spaces ⋮ Metrizability of minimal and unbounded topologies ⋮ Spaces of $u\tau$-Dunford-Pettis and $u\tau$-Compact Operators on Locally Solid Vector Lattices ⋮ Unbounded topologies and \textit{uo}-convergence in locally solid vector lattices ⋮ Unbounded \(p\)-convergence in lattice-normed vector lattices ⋮ Compact-like operators in lattice-normed spaces ⋮ Nonstandard hulls of lattice-normed ordered vector spaces ⋮ Unbounded absolute weak convergence in Banach lattices ⋮ \(um\)-topology in multi-normed vector lattices ⋮ \(u\tau \)-convergence in locally solid vector lattices ⋮ Неограниченные сходимости в конвергентных векторных решетках ⋮ The Banach-Saks property from a locally solid vector lattice point of view ⋮ On the Brezis–Lieb Lemma and Its Extensions

Cites Work

• Unbounded norm topology in Banach lattices
• Measures of non-compactness of operators on Banach lattices
• Duality for unbounded order convergence and applications
• Unbounded norm topology beyond normed lattices
• Unbounded norm convergence in Banach lattices
• Compact-like operators in lattice-normed spaces
• Some loose ends on unbounded order convergence
• Unbounded absolute weak convergence in Banach lattices
• \(um\)-topology in multi-normed vector lattices
• Unbounded order convergence in dual spaces
• Topological aspects of order in \(C(X)\)
• Unbounded order convergence and application to martingales without probability
• Uo-convergence and its applications to Cesàro means in Banach lattices
• Closedness of convex sets in Orlicz spaces with applications to dual representation of risk measures
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