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31 December 2001 Set quantities and Tauberian operators
Sergio Falcon, Kishin Sadarangani
Abstr. Appl. Anal. 6(7): 431-440 (31 December 2001). DOI: 10.1155/S1085337501000641


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.


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Sergio Falcon. Kishin Sadarangani. "Set quantities and Tauberian operators." Abstr. Appl. Anal. 6 (7) 431 - 440, 31 December 2001.


Published: 31 December 2001
First available in Project Euclid: 13 April 2003

zbMATH: 1028.46009
MathSciNet: MR1879575
Digital Object Identifier: 10.1155/S1085337501000641

Primary: 46A25 , 46A50
Secondary: 46B10

Rights: Copyright © 2001 Hindawi

Vol.6 • No. 7 • 31 December 2001
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