Characterizing filters by convergence (with respect to filters) in Banach spaces

DOI10.1016/j.topol.2011.11.004zbMath1245.46006OpenAlexW2046397091MaRDI QIDQ409602

H. S. Pino-Villela, Salvador García-Ferreira

Publication date: 13 April 2012

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2011.11.004

zbMATH Keywords

Schauder basisBanach space\(P\)-filter\(P\)-filter\(^{+}\)\(Q\)-filter\(Q\)-filter\(^{+}\)Schur filterselective filterselective\(^{+}\) filterweak \(P\)-filterweak \(Q\)-filterweakly selective filter

Mathematics Subject Classification ID

Classical Banach spaces in the general theory (46B25) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Summability in abstract structures (40J05)

Related Items

The set of filter cluster functions ⋮ Filter-dependent versions of the uniform boundedness principle

Cites Work

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• On bases and unconditional convergence of series in Banach spaces
• An Introduction to Banach Space Theory
• The Schur l1 Theorem for filters
• Sums of ultrafilters
• A new kind of compactness for topological spaces
• Partial Orders on the Types in βN
• Biorthogonal systems in Banach spaces

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