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Titlebook: Linear Operators and Approximation II / Lineare Operatoren und Approximation II; Proceedings of the C P. L. Butzer,B. Szőkefalvi-Nagy Confe

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Characterization of Intermediate Spaces of Mϕ Spaces type. This paper serves to provide a solution for M. spaces which appear in fundamental roles in classical interpolation theorems such as the Marcinkiewicz and Stein-Weiss theorems ([1], [2], [10]) as well as in the class of rearrangement invariant Banach function spaces ([6], [8]).
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Approximation mit Polynomoperatorentoren auf E, d.h. die Menge der Linearkombinationen von stetigen Operatoren T mit endlichdimensionalem Wertebereich, welche von der Form T(x)=S(x,...,x), x∈E, sind, wobei die S k-lineare Operatoren sind (im reellen Fall) oder analoge Operatoren die in jedem Argument linear oder antilinear sein können (im komplexen Fall).
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On the Comparison of Approximation Processes in Banach Algebrasthe kernels, it seems to be natural to look on this section of approximation theory from the point of view of abstract Banach algebras, particularly since the Gelfand transform may be used as a substitute for integral transforms, the most effective tool in the classical setting.
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On Comparison Theorems for Generalized Moduli of Continuityr our theorem implies the known fact that the order of best approximation by trigonometric polynomials for any continuous and periodic function f satisfies E. (f) = .((log n).) if and only if the modulus of continuity of f is .(|log t|.).
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