Timeline for Example of an infinite dimensional reflexive Banach algebra
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 28, 2014 at 6:49 | comment | added | Joakim Arnlind | Yes, there is a reason :) I'm doing some potential theory on normed spaces, and wanted a couple of concrete examples of spaces which are NOT algebras of functions. | |
| Feb 27, 2014 at 5:03 | comment | added | Yemon Choi | Was there any reason why you wanted it non-commutative? There are semisimple commutative Banach algebras with no non-trivial idempotents that are isomorphic to Hilbert spaces. | |
| Feb 7, 2014 at 21:59 | vote | accept | Joakim Arnlind | ||
| Feb 7, 2014 at 0:31 | answer | added | Eusebio Gardella | timeline score: 10 | |
| Feb 6, 2014 at 9:50 | comment | added | UwF | Just take a reflexive Banach space and turn it into a Banach algebra by setting 1) $xy=0$ for all $x,y$, 2) $xy=\phi(x)y$ with some functional $\phi$ with $||\phi||\le 1$, 3) add a unit to example 2). I guess none of these would be "nice"... and 1) isn't even noncommutative. | |
| Feb 6, 2014 at 8:56 | comment | added | Narutaka OZAWA | I don't know how nice it is, but the algebra of Hilbert--Schmidt operators is a Hilbert space as a Banach space. | |
| Feb 6, 2014 at 8:50 | history | asked | Joakim Arnlind | CC BY-SA 3.0 |