Timeline for spectral sections - explicit construction
Current License: CC BY-SA 2.5
3 events
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| Feb 17, 2010 at 16:13 | comment | added | Paul | A couple of thoughts: if the spectral projections $\Pi_\beta$ are all compact perturbations of each other, you are considering maps from B to the Grassmanian of projections that differ from a fixed $\Pi_{\beta{0}}$ by a compact operator. There is a literature on this: e.g. Chapter 15 of Booss-Wociechowski. Another thought: if your family of Dirac operators is a family on $\partial M$ and you can extend them over $M$ then the Calderon projectors for the extensions (explained in [BW]) gives you a spectral section, and varying the operators on the interior gives you many. | |
| Feb 17, 2010 at 10:59 | comment | added | J Fabian Meier | Thank you so far. The spectral gap thing was already clear to me. I will think about your second sugestion. My request for examples was also meant to help me with the following thing: It is known that the existence of one spectral section implies the existence of infinitely many of them. So I am looking for a space with "many" known spectral sections to gain insight into their relation. | |
| Feb 17, 2010 at 0:37 | history | answered | Paul | CC BY-SA 2.5 |