Timeline for When LCS is isomorphic to subspace of some function space?
Current License: CC BY-SA 3.0
4 events
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| Jul 24, 2014 at 7:17 | comment | added | blackburne | You can always realise it as a subspace of the space of continuous functions on the dual by using the topology of uniform convergence on the equicontinuous sets of the latter, raher than the weak topology. | |
| Apr 29, 2012 at 13:34 | comment | added | Nik Weaver | You're right, I should have read the question more carefully. Not every LC topology is induced by a family of linear functionals --- for instance, if a topology is induced by a family of linear functionals then every open neighborhood of zero contains a finite codimension subspace. I guess the answer is that you can realize a LCTVS in this sense as a function space if and only if its original topology equals its weak topology. I'm not sure there's going to be any more concrete answer than that. | |
| Apr 29, 2012 at 12:35 | comment | added | Gerald Edgar | ... but why is the original LC topology equal to the product topology of the function space ??? | |
| Apr 29, 2012 at 2:37 | history | answered | Nik Weaver | CC BY-SA 3.0 |