On compactness in \(L_p(\mu,X)\) in the weak topology and in the topology \(\sigma(L_p(\mu,X),L_q(\mu,X'))\)

DOI10.1007/BF01179760zbMath0491.46010MaRDI QIDQ5966539

Wolfgang Hiermeyer, Jürgen Batt

Publication date: 1983

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173294

zbMATH Keywords

Eberlein-Smulian theoremcountably compactRadon-Nikodym propertysequentially compactspace of Bochner integrable functionsrelatively compact

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) Classical Banach spaces in the general theory (46B25) Vector-valued measures and integration (46G10) Radon-Nikodým, Kre?n-Milman and related properties (46B22) Compactness in topological linear spaces; angelic spaces, etc. (46A50)

Related Items (17)

Weak compactness and uniform convergence of operators in spaces of Bochner integrable functions ⋮ Nets and sequences of \(p\)-Bochner, \(p\)-Dunford and \(p\)-Pettis integrable functions with values in a Banach space ⋮ On Banach spaces with Mazur's property ⋮ On weak compactness in Lebesgue-Bochner spaces ⋮ Strongly Asplund generated and strongly conditionally weakly compactly generated Banach spaces ⋮ On (V*) sets and Pelczynski's property (V*) ⋮ The Mazur property and completeness in the space of Bochner-integrable functions L₁(μ, X) ⋮ On the SWCG property in Lebesgue-Bochner spaces ⋮ Weakly \(p\)-Dunford Pettis sets in \(L_1(\mu,X)\) ⋮ Eberlein compactness ⋮ Conditional weak compactness in vector-valued function spaces ⋮ A class of weakly compact sets in Lebesgue-Bochner spaces ⋮ Weak compactness in Köthe-Bochner spaces and Orlicz-Bochner spaces ⋮ On a three-space property for Lindelöf \(\Sigma\)-spaces, (WCG)-spaces and the Sobczyk property ⋮ Bases of random unconditional convergence in Banach spaces ⋮ Hereditary properties for duals of Bochner \(L_p\)-function-spaces ⋮ $\varepsilon $-weakly precompact sets in Banach spaces

Cites Work

• An averaging result for \(l^ 1-\)sequences and applications to weakly conditionally compact sets in \(L^ 1\).
• Weak compactness in spaces of Bochner integrable functions and applications
• Integral representation of dominated operations on spaces of continuous vector fields
• A general bilinear vector integral
• Remarks on Weak Compactness in L₁(μ,X)
• Point-Wise Compact Subsets of the First Baire Class
• Weakly compact operators from a B-space into the space of Bochner integrable functions
• Produits tensoriels topologiques et espaces nucléaires
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