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
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