On the density of Banach spaces 𝐶(𝐾) with the Grothendieck property

DOI10.1090/S0002-9939-06-08401-2zbMath1105.03046arXiv1005.3524MaRDI QIDQ3419952

Christina Brech

Publication date: 1 February 2007

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

Full work available at URL: https://arxiv.org/abs/1005.3524

zbMATH Keywords

consistencyforcingBoolean algebrasGrothendieck spaceBanach space of continuous functionsseparation propertiesset-theoretic assumption

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Consistency and independence results (03E35)

Related Items (12)

The Nikodym property and cardinal characteristics of the continuum ⋮ Independent families in Boolean algebras with some separation properties ⋮ The Nikodym property in the Sacks model ⋮ On Efimov spaces and Radon measures ⋮ Convergence of measures after adding a real ⋮ A simple Efimov space with sequentially-nice space of probability measures ⋮ Grothendieck $C(K)$-spaces and the Josefson–Nissenzweig theorem ⋮ On weak*-extensible Banach spaces ⋮ On the existence of overcomplete sets in some classical nonseparable Banach spaces ⋮ Grothendieck spaces: the landscape and perspectives ⋮ Convergence of measures in forcing extensions ⋮ Minimally generated Boolean algebras and the Nikodym property

Cites Work

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• A non-reflexive Grothendieck space that does not contain \(l_{\infty }\)
• Sacks forcing and the total failure of Martin's axiom
• Topics in the theory of complemented subspaces in Banach spaces
• Un nouveau \(C(K)\) qui possède la propriété de Grothendieck
• Remarks on cofinalities and homomorphism types of Boolean algebras
• The Vitali-Hahn-Saks Theorem for Boolean Algebras with the Subsequential Interpolation Property
• On Sequences without Weak ∗ Convergent Convex Block Subsequences
• On relatively disjoint families of measures, with some applications to Banach space theory

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