On the extension of linear operators
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 exa...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201006998 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |