Timeline for Topology on the space of Schwartz Distributions
Current License: CC BY-SA 3.0
5 events
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| Nov 6, 2011 at 1:26 | history | edited | Sergei Akbarov | CC BY-SA 3.0 |
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| Nov 6, 2011 at 1:21 | comment | added | Sergei Akbarov | Of course, compact-open topology on the space of operators is locally convex. But not likely nuclear, barreled or Frechet... Maybe for operators on S this is true, but I do not know. | |
| Nov 6, 2011 at 0:16 | comment | added | Jonathan Gleason | In particular, as a start, a description of the compact-open topology on this space of operators would be nice. Is the resulting topology locally convex, do we get a nuclear space, a barelled space, a Frechet space, etc.? Honestly, I have not thought much about the problem of describing the topology myself yet as I figured there are probably entire sources out there on this and/or related topics . . . | |
| Nov 6, 2011 at 0:12 | comment | added | Jonathan Gleason | Well, the idea "abstractly characterize" is not a precisely defined, but I'll try to give you an idea of what I meant by way of example. If you take a subalgebra of bounded operators on a Hilbert space, this is a unital $C^*$-algebra. Similarly, the Gelfand-Naimark Theorem says that any abstract unital $C^*$-algebra is isomorphic to a subalgebra of all the bounded operators on some Hilbert space. In this way, the structure of a unital $C^*$-algebra abstractly characterizes bounded observables on a Hilbert space. Can something similar be done in this case? | |
| Nov 5, 2011 at 23:39 | history | answered | Sergei Akbarov | CC BY-SA 3.0 |