International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 10, Pages 621-623
doi: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 John J. Saccoman. 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.