Abstract
It is shown that in the classical uniform boundedness principle the condition of strong (pure) boundedness of a sequence of bounded linear operators on a Banach space X may indeed be replaced by boundedness with rates on corresponding subsets of X. The method of proof employed is the gliding hump method but now equipped with rates. Some applications are given to linear polynomial convolution operators, regaining and extending relevant work of Dahmen — Görlich 1974 and Baskakov 1977.
The contribution of this author was supported by Grant No. II B4 FA 7888 awarded by the Minister für Wissenschaft und Forschung des Landes NRW.
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Dickmeis, W., Nessel, R.J. (1981). A Uniform Boundedness Principle with Rates and an Application to Linear Processes. In: Butzer, P.L., Sz.-Nagy, B., Görlich, E. (eds) Functional Analysis and Approximation. ISNM 60: International Series of Numerical Mathematics / ISNM 60: Internationale Schriftenreihe zur Numerischen Mathematik / ISNM 60: Série internationale d’Analyse numérique, vol 60. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9369-5_28
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DOI: https://doi.org/10.1007/978-3-0348-9369-5_28
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