Copies of 𝑐₀ and ℓ_{∞} in topological Riesz spaces

DOI10.1090/S0002-9947-98-02157-6zbMath0903.46010OpenAlexW1523954491MaRDI QIDQ4211112

Iwo Labuda, Drewnowski, Lech

Publication date: 10 September 1998

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-98-02157-6

zbMATH Keywords

Orlicz-Pettis theoremcopy of \(c_{0}\)Levi propertyspace of measurable functionsLebesgue propertytopological Riesz spacecopy of \(\ell_{\infty}\)

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) Vector-valued set functions, measures and integrals (28B05) Ordered topological linear spaces, vector lattices (46A40) Convergence and divergence of infinite limiting processes (40A99)

Related Items

Completeness of unbounded convergences ⋮ \(L^{1}(\mu)\) for vector-valued measure \(\mu\) ⋮ On the Levi and Lebesgue properties ⋮ On some topological properties of vector-valued function spaces ⋮ Solid sequence \(F\)-spaces of \(L_{0}\)-type over submeasures on \(\mathbb N\) ⋮ THE FATOU COMPLETION OF A FRÉCHET FUNCTION SPACE AND APPLICATIONS ⋮ Copies of \(\mathbb R^{\mathbb N}\) in F-lattices ⋮ Rosenthal L∞-theorem revisited ⋮ Weak completeness properties of the $L^1 $-space of a spectral measure

Cites Work

• Submeasures and locally solid topologies on Riesz spaces
• Order completeness and disjoint completeness of linear partially ordered spaces
• On Levi-Like Properties and some of Their Applications in Riesz Space Theory
• Exhaustive operators and vector measures
• On Schwartz's C-spaces and Orlicz's O-spaces
• The Orlicz-Pettis theorem for topological Riesz spaces
• On relatively disjoint families of measures, with some applications to Banach space theory
• On a class of asymptotically divergent sequences of functions
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