Abstract and Applied Analysis
Volume 6 (2001), Issue 7, Pages 431-440
doi:10.1155/S1085337501000641
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 Sergio Falcon and Kishin Sadarangani. 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.
Abstract
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.