December 2022 Quantifications of boundedly complete and shrinking bases
Dongyang Chen, Tomasz Kania, Yingbin Ruan
Author Affiliations +
Illinois J. Math. 66(4): 627-645 (December 2022). DOI: 10.1215/00192082-10261081

Abstract

In the present paper, we’ll introduce quantities measuring how far a (Schauder) basis is from being boundedly complete or shrinking. These quantities will be proved to really measure nonbounded completeness or nonshrinkingness of bases by investigating many bases. As applications, they will be used to prove quantitative versions of the well-known relationships between shrinking bases and boundedly complete bases due to R. C. James.

Citation

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Dongyang Chen. Tomasz Kania. Yingbin Ruan. "Quantifications of boundedly complete and shrinking bases." Illinois J. Math. 66 (4) 627 - 645, December 2022. https://doi.org/10.1215/00192082-10261081

Information

Received: 30 June 2022; Revised: 7 October 2022; Published: December 2022
First available in Project Euclid: 9 November 2022

MathSciNet: MR4565345
zbMATH: 1511.46010
Digital Object Identifier: 10.1215/00192082-10261081

Subjects:
Primary: 46B03
Secondary: 46B15

Rights: Copyright © 2022 by the University of Illinois at Urbana–Champaign

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Vol.66 • No. 4 • December 2022
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