Quantifications of boundedly complete and shrinking bases

DOI10.1215/00192082-10261081OpenAlexW4312368426MaRDI QIDQ2103561

Yingbin Ruan, Tomasz Kania, Dong Yang Chen

Publication date: 14 December 2022

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/illinois-journal-of-mathematics/volume-66/issue-4/Quantifications-of-boundedly-complete-and-shrinking-bases/10.1215/00192082-10261081.full

zbMATH Keywords

Schauder basesshrinking basesboundedly complete bases

Mathematics Subject Classification ID

Isomorphic theory (including renorming) of Banach spaces (46B03) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15)

Cites Work

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• On quantification of weak sequential completeness
• An extension of the Krein--Smulian theorem
• Measures of weak noncompactness in Banach spaces
• Quantitative Dunford-Pettis property
• Quantification of the Banach-Saks property
• The quantitative difference between countable compactness and compactness
• Measures of weak non-compactness in spaces of nuclear operators
• Expansions in Banach spaces
• Bases and reflexivity of Banach spaces
• On a difference between quantitative weak sequential completeness and the quantitative Schur property
• A quantitative version of James's Compactness Theorem
• Quantification of the reciprocal Dunford–Pettis property
• The distance $dist (\mathcal{B},X)$ when $\mathcal{B}$ is a boundary of $B(X^{**})$
• A CHARACTERIZATION OF SUBSPACES OF WEAKLY COMPACTLY GENERATED BANACH SPACES
• Shrinking Bases in Banach Spaces
• Some curious bases for $c_{0}$ and C[0,1]