Timeline for Why is this operator compact?
Current License: CC BY-SA 3.0
2 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 4, 2013 at 18:11 | comment | added | Branimir Ćaćić | Would you happen to know, by any chance, when $0$ can be an isolated point in the spectrum of the Dirac operator on a complete but non-compact spin manifold? Because then one could still use the spectral triples convention of replacing $g(t) = |t|^{-n}$ with some $\tilde{g} \in C_0(\mathbb{R})$ with $\tilde{g}(t) = g(t) = |t|^{-n}$ for $|t|>\epsilon$ and $\tilde{g}(0) = 0$, where $\sigma(D) \cap [-\epsilon,\epsilon] = \{0\}$. Otherwise, I suppose one would have no choice but too use, rather, something like $g(t) = (1+|t|)^{-n}$ to make things work? | |
| Jul 4, 2013 at 17:15 | history | answered | Paul Siegel | CC BY-SA 3.0 |