Timeline for When do positive operators have eigenvalues?
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| Feb 15, 2021 at 22:28 | comment | added | Jochen Glueck | @ConstantinK: Thanks for your response! Unfortunately, I am not aware of general methods to show the existence of eigenvalues without spectral gaps. A lot has certainly been done in this direction for stochastic operators on $L^1$ (in the context of Markov chains), but I don't know to what extent this problem has been studied for self-adjoint operators on $L^2$-spaces (without any a priori assumption that the operator be stochastic in any sense). Concering the more specific setting in your edit: I guess I can't be of much help here, since this is not my field of expertise. | |
| Feb 15, 2021 at 21:44 | comment | added | Constantin K | Interesting - many thanks! In the case that interests me the condition is unfortunately not satisfied and if one could prove a spectral gap that would be a very interesting result that is likely to be not achievable by such general methods. Are you aware of any other results of a similar type that might only focus on proving the existence of an eigenvalue? | |
| Feb 15, 2021 at 19:30 | history | answered | Jochen Glueck | CC BY-SA 4.0 |