Quantitative extensions of the uniform boundedness principle (Q1096828)

During the past decade the authors have developed a functional analytic approach to the problem of the sharpness of the various concrete error bounds arising in approximation theory and numerical analysis. See the monograph of the first two authors [Quantitative Prinzipien gleichmäßiger Beschränktheit und Schärfe von Fehlerabschätzungen, Forchungsber. Landes Nordrhein-Westfalen 3117, 110 S. (1982; Zbl 0493.41045)]. The purpose of this paper is to survey recent results in the subject.