Timeline for Compact operator without eigenvalues?
Current License: CC BY-SA 4.0
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| Jul 10, 2020 at 11:10 | comment | added | Nik Weaver | Well, under what assumptions? My construction works for your operator with any sequence in $c_0(\mathbb{Z})$ in place of $(\mu_n)$. In general every nonzero element of the spectrum of a compact operator is an eigenvalue, but there do exist compact operators with spectrum $\{0\}$ and no eigenvalues. | |
| Jul 10, 2020 at 10:37 | comment | added | Landauer | Thank you also for your answer. Since Mateusz answered a few minutes earlier, I just accepted his answer, I hope this is okay. But let me also ask you, if you see any abstract argument that there have to be eigenvalues (so not by explicitly diagonalization) but by some a priori argument? | |
| Jul 10, 2020 at 9:30 | history | answered | Nik Weaver | CC BY-SA 4.0 |