Set quantities and Tauberian operators
Summary: The concept of convexity plays an important role in the classical geometry of normed spaces and it is frequently used in several branches of nonlinear analysis. In recent years some papers that contain generalizations of the concept of convexity with the help of measures of noncompactness have appeared. The Tauberian operators were introduced by \textit{N. Kalton} and \textit{A. Wilansky} [Proc. Am. Math. Soc. 57, 251-255 (1976; Zbl 0304.47023)] and they appear in the literature with the aim of responding to some questions related to the summability and the factorization of operators; in the preservation by isomorphisms in Banach spaces, and so forth. In this paper we make the study of the Tauberian operators, not starting from the Euclidean distance, but by means of general set quantities.
scientific article; zbMATH DE number 1750238