Timeline for Why is index unchanged after applying functional calculus?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Nov 8, 2017 at 0:34 | vote | accept | geometricK | ||
| Nov 7, 2017 at 19:05 | comment | added | Paul Siegel | @ogoah You might check out chapter 10 of Analytic K-homology by Higson-Roe. They show that every elliptic operator determines a K-homology class via the functional calculus, and that the index depends only on this class. The book is written with generalizations to Hilbert modules in mind, though they don't appear explicitly. And yes, the whole construction is in a sense a jazzed-up version of what I wrote above. | |
| Nov 7, 2017 at 12:27 | comment | added | geometricK | Thanks. I'm not quite sure if this technique adapts to the the setting I have in mind, which is Hilbert modules. But if there is a spectral decomposition theorem of Hilbert modules for regular self-adjoint operators, it could work. | |
| Nov 7, 2017 at 12:21 | vote | accept | geometricK | ||
| Nov 7, 2017 at 12:22 | |||||
| Nov 7, 2017 at 3:21 | history | answered | Paul Siegel | CC BY-SA 3.0 |