ErrataApplied Analysis(Corrected in online files but not in Second Printing)•p.115: Replace statement of Theorem 5.53 with: “A consistent ap-proximation scheme is convergent if and only if it is stable.”•p.115: Replace last paragraph (“Conversely...”)of the proof of The-orem 5.53 with:“Conversely, we prove that a convergent scheme isstable.For anyf∈Y, letu=A-1f.Then, since the scheme isconvergent, we haveu→uas→0, whereu=A-1f, so thatuis bounded. Thus, there exists a constantMf, independent of, suchthatkA-1fk ≤Mf. The uniform boundedness theorem, which we donot prove here, then implies that there exists a constant
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