Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series

DOI10.1023/A:1022481016009zbMath1079.46505OpenAlexW191284434MaRDI QIDQ3366546

F. Benítez-Trujillo, F. J. Pérez-Fernández, Antonio Aizpuru

Publication date: 14 February 2006

Published in: Czechoslovak Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1022481016009

zbMATH Keywords

completenessbarrellednessweakly unconditionally Cauchy series

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Banach sequence spaces (46B45)

Related Items (11)

Unconditionally Cauchy series and Cesàro summability ⋮ On the Kreĭn-Milman property and the Bade property ⋮ On Cesàro summability of vector valued multiplier spaces and operator valued series ⋮ Vector valued multiplier spaces of \(f_\lambda \)-summability, completeness through \(c_0(X)\)-multiplier convergence and continuity and compactness of summing operators ⋮ Operator valued series, almost summability of vector valued multipliers and (weak) compactness of summing operator ⋮ Multiplier Sequence Spaces Defined by Statistical Summability and Orlicz-Pettis Theorem ⋮ Matrix summability methods and weakly unconditionally Cauchy series ⋮ A generalization of almost convergence, completeness of some normed spaces with wuC series and a version of Orlicz-Pettis theorem ⋮ Completeness of a normed space via strong p-Cesàro summability ⋮ On some vector valued multiplier spaces with statistical Cesàro summability ⋮ Weakly unconditionally Cauchy series and Fibonacci sequence spaces

Cites Work

• Unnamed Item
• Unconditionally convergent series of operators on Banach spaces
• Locally convex spaces containing no copy of \(c_ 0\)
• On Relationships Amongst Certain Spaces Of Sequences In An Arbitrary Banach Space
• On bases and unconditional convergence of series in Banach spaces
• Spaces of \(S\)-bounded multiplier convergent series

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