Josefson-Nissenzweig property for \(C_p\)-spaces

DOI10.1007/s13398-019-00667-8zbMath1437.46029arXiv1809.07054OpenAlexW3102138077MaRDI QIDQ2331686

Jerzy Kąkol, Wiesław Śliwa, Taras Banakh

Publication date: 30 October 2019

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.07054

zbMATH Keywords

spaces of continuous functionsseparable quotient problemJosefson-Nissenzweig theoremquotient spacesEfimov space

Mathematics Subject Classification ID

Function spaces in general topology (54C35) Topological linear spaces of continuous, differentiable or analytic functions (46E10)

Related Items (12)

Continuous linear images of spaces \(C_p(X)\) with the weak topology ⋮ Descriptive topology for analysts ⋮ Metrizable quotients of free topological groups ⋮ Grothendieck $C(K)$-spaces and the Josefson–Nissenzweig theorem ⋮ On subspaces of spaces \(C_p(X)\) isomorphic to spaces \(c_0\) and \(\ell_q\) with the topology induced from \(\mathbb{R}^{\mathbb{N}}\) ⋮ On complemented copies of the space c₀ in spaces Cp(X,E)$C_p(X,E)$ ⋮ On linear continuous operators between distinguished spaces \(C_p(X)\) ⋮ Witnessing the lack of the Grothendieck property in \(C(K)\)-spaces via convergent sequences ⋮ On weakly compact sets in \(C\left( X\right) \) ⋮ A note on the weak topology of spaces \(C_k(X)\) of continuous functions ⋮ \(C _p\)-spaces dominated by metrizable topologies ⋮ On complemented copies of the space \(c_0\) in spaces \(C_p(X \times Y)\)

Cites Work

• Banach spaces of continuous functions as dual spaces
• Completeness properties of function spaces
• Banach spaces of vector-valued functions
• Metrizable quotients of \(C_p\)-spaces
• Efimov spaces and the separable quotient problem for spaces \(C_{p}(K)\)
• On quasi-complemented subspaces of Banach spaces, with an appendix on compactness of operators from \(L^{p}(\mu)\) to \(L^{r}(\nu)\)
• On the separable quotient problem for Banach spaces
• A COMPACT HAUSDORFF SPACE ALL OF WHOSE INFINITE CLOSED SUBSETS ARE $ n$-DIMENSIONAL
• Separable quotients in 𝐶_{𝑐}(𝑋), 𝐶_{𝑝}(𝑋), and their duals
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