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: John J. Saccoman
Format: Article
Language:English
Published: Wiley 2001-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171201006998
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author John J. Saccoman
author_facet John J. Saccoman
author_sort John J. Saccoman
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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.
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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