Unconditionally convergent series of operators on Banach spaces

DOI10.1006/JMAA.1997.5218zbMath0891.46011OpenAlexW2095213524MaRDI QIDQ1353746

Congxin Wu, Qingying Bu

Publication date: 20 July 1998

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1997.5218

zbMATH Keywords

vector-valued sequencescharacterization of relatively compact subsetsspace of bounded multiplier convergent seriesunconditionally convergent in the uniform operator topologyunconditionally convergent in the weak operator topology

Mathematics Subject Classification ID

Spaces of vector- and operator-valued functions (46E40) Spaces of operators; tensor products; approximation properties (46B28) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Compactness in topological linear spaces; angelic spaces, etc. (46A50)

Related Items (8)

Matrix summability and uniform convergence of series ⋮ Boolean algebras and uniform convergence of series ⋮ Banach limits and uniform almost summability ⋮ Vector-valued almost convergence and classical properties in normed spaces ⋮ Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series ⋮ A Riemann type theorem for series of operators on Banach spaces ⋮ Vector-valued spaces of multiplier statistically convergent series and uniform convergence ⋮ Spaces of \(\lambda\)-multiplier convergent series

Cites Work

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• The Schur and Hahn theorems for operator matrices
• The Schur lemma for bounded multiplier convergent series
• Locally convex spaces containing no copy of \(c_ 0\)
• On bases and unconditional convergence of series in Banach spaces
• A Riemann Type Theorem for Unconditional Convergence of Operators
• Absolute and Unconditional Convergence in Normed Linear Spaces

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