Timeline for Is there dual space of the distributions $\mathcal{D}'(R)$?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 28, 2016 at 22:23 | comment | added | reuns | (LF means en.wikipedia.org/wiki/LF-space) | |
| Feb 8, 2012 at 9:49 | vote | accept | Anand | ||
| Feb 8, 2012 at 9:48 | comment | added | Anand | Thanks Stefan and Jochen, I agree. Actually, in Yoshida's book, the reflexiveness of a locally convex linear topology space $X$ is defined with respect to strong topology: $X= (X_s')_s'$. Thanks a lot for your answer and clarification. :-) | |
| Feb 8, 2012 at 9:03 | comment | added | Jochen Wengenroth | The weak$^*$ topology hardly ever coincides with the topology of uniform convergence on bounded sets as described in Stefan's answer. This is the case if and only if all bounded sets are finite-dimensional. | |
| Feb 8, 2012 at 9:01 | comment | added | Jochen Wengenroth | For any topological vector space $X$ the dual of $(X',\sigma(X',X))$ is $X$ (more precisely, given by an evaluation in some point of $X$). This is rather linear algebra than topological vector spaces: If $F$ is a continuous linear functional on $X'$ there are finitely many $x_n \in X$ and a constant $C$ such that [ |F(\phi)|\le C \max\{\phi(x_n)\} ] which implies that $F$ is a linear combination of the evaluations in $x_n$ and (by linearity) an evaluation in the linear combination of the $x_n$. | |
| Feb 7, 2012 at 18:35 | comment | added | Stefan Waldmann | Hi Johannes: Ok, that I didn't know. But the weak$^*$ topology is still different from the strong one, right? I should be strictly weaker... | |
| Feb 7, 2012 at 18:19 | comment | added | Johannes Hahn | The dual of the weak*-space can is also isomorphic (via the natural map) to the space of test functions. | |
| Feb 7, 2012 at 17:37 | history | answered | Stefan Waldmann | CC BY-SA 3.0 |