Timeline for Simultaneously extending the functionals of a subspace of a Banach space to the whole space
Current License: CC BY-SA 3.0
6 events
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| Mar 20, 2014 at 14:35 | comment | added | Yemon Choi | Having a Schauder basis still might not save you; see Bill Johnson's answer. Note that every Banach space $Y$ embeds isometrically into some $X=\ell^\infty(\Gamma)$, but it is relatively rare that $Y^\perp$ will be complemented in $X^*$. | |
| Mar 20, 2014 at 14:18 | history | edited | smyrlis | CC BY-SA 3.0 |
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| Mar 20, 2014 at 14:11 | answer | added | Bill Johnson | timeline score: 8 | |
| Mar 20, 2014 at 14:09 | comment | added | Marc Palm | Be careful, there exists Banach spaces which do not admit a Schauder Basis. The first examples are due to Enflo. | |
| Mar 20, 2014 at 14:08 | comment | added | Marc Palm | There are results available, when the extension is unique, e.g. in a Hilbert space or more general results can be found here jstor.org/discover/10.2307/…. Of course, Hamel basis are not to be chosen in topological vector space, e.g. for Banach spaces one works with a Schauder basis. | |
| Mar 20, 2014 at 13:53 | history | asked | smyrlis | CC BY-SA 3.0 |