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International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 10, Pages 621-623
http://dx.doi.org/10.1155/S0161171201006998

On the extension of linear operators

Department of Mathematics and Computer Science, Seton Hall University, South Orange 07079, NJ, USA

Received 7 March 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.

Abstract

It is well known that the Hahn-Banach theorem, that is, the extension theorem for bounded linear functionals, is not true in general for bounded linear operators. A characterization of spaces for which it is true was published by Kakutani in 1940. We summarize Kakutani's work and we give an example which demonstrates that his characterization is not valid for two-dimensional spaces.