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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1849307227919220736 |
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| author | John J. Saccoman |
| author_facet | John J. Saccoman |
| author_sort | John J. Saccoman |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-26833a4e0ba64540bb368fbd112e41e3 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-26833a4e0ba64540bb368fbd112e41e32025-08-20T03:54:48ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-01281062162310.1155/S0161171201006998On the extension of linear operatorsJohn J. Saccoman0Department of Mathematics and Computer Science, Seton Hall University, South Orange 07079, NJ, USAIt 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.http://dx.doi.org/10.1155/S0161171201006998 |
| spellingShingle | John J. Saccoman On the extension of linear operators International Journal of Mathematics and Mathematical Sciences |
| title | On the extension of linear operators |
| title_full | On the extension of linear operators |
| title_fullStr | On the extension of linear operators |
| title_full_unstemmed | On the extension of linear operators |
| title_short | On the extension of linear operators |
| title_sort | on the extension of linear operators |
| url | http://dx.doi.org/10.1155/S0161171201006998 |
| work_keys_str_mv | AT johnjsaccoman ontheextensionoflinearoperators |