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Abstract and Applied Analysis
Volume 6 (2001), Issue 7, Pages 431-440

Set quantities and Tauberian operators

Department of Mathematics, University of Las Palmas de Gran Canaria, Las Palmas 35017, Spain

Received 6 July 2001

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 the measures of noncompactness have appeared. The Tauberian operators were introduced by Kalton and Wilansky (1976) and they appear in the literature with the aim of responding to some questions related with 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.