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International Journal of Mathematics and Mathematical Sciences
Volume 13, Issue 2, Pages 271-273
http://dx.doi.org/10.1155/S0161171290000394

A note on Tauberian operators

1Departamento de Matemáticas, ETSI Industriales, Universidad de Oviedo, Castiello de Bernueces, Gijón 33204, Spain
2Departamento de Matemáticas, Facultad de Ciencias, Universidad de Santander, Av. Los Castros, Santander 39071, Spain

Received 20 May 1988; Revised 23 August 1988

Copyright © 1990 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.

Abstract

In this note we prove the existence of operators which are not Tauberian even though they satisfy properties about restrictions being Tauberian. The operators are defined on Banach spaces which contain a somewhat reflexive, non-reflexive subspace. This gives an answer to a question proposed by R. Neidinger [1].