Timeline for Schur's Lemma for Hilbert spaces
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 11, 2015 at 11:16 | vote | accept | David E Speyer | ||
| Aug 10, 2015 at 3:12 | comment | added | Yemon Choi | Indeed: it is known that the analogue of Schur's theorem for unitary, topologically irreducible representations is true, i.e. the commutant of the representation is trivial. The proof is, I imagine, essentially the one you have just given, and my guess is that it should be somewhere in the second half of Dixmier's Cstar algebras book (among many other likely sources) | |
| Aug 10, 2015 at 3:11 | comment | added | Yemon Choi | The spectral projections should also commute with $G$, and hence be either $0$ or $I$ by the assumption of topological irreducibility. | |
| Aug 10, 2015 at 1:47 | history | answered | Eric Wofsey | CC BY-SA 3.0 |