Quantifications of boundedly complete and shrinking bases (Q2103561)

The authors introduce quantities measuring how far a Schauder basis is from being boundedly complete or shrinking. These quantities are used to measure nonbounded completeness or nonshrinkingness of bases for several examples. A relationship between the basis constant and these quantities is built. The motivation of the paper is to prove quantitative versions of the well-known relationships between shrinking bases and boundedly complete bases due to R.~C. James.