Timeline for Existence of the eigenvalue of the dual operator of the transfer operator
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| Aug 7, 2019 at 20:28 | comment | added | Jochen Glueck | @AnthonyQuas: Well, the argument in the quote certainly refers to what you write in your comment. Still, if one likes cones, one can also argue as follows: Given that the space of contiunous functions $C(K)$ on a compact space $K$ has a normal cone with non-empty interior, it follows, for every positive operator $T$ on $C(K)$, that the spectral radius of $T$ is an eigenvalue of the dual operator $T^*$. | |
| Aug 7, 2019 at 19:47 | comment | added | Anthony Quas | I think there is no normal cone here, but instead compactness of the unit ball in the weak* topology (and continuity of $\mathcal L^*$ in that topology. | |
| Aug 7, 2019 at 2:42 | history | asked | Ilovemath | CC BY-SA 4.0 |