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Topic:
Invariant subspace problem solved?
Replies:
9
Last Post:
Mar 6, 2013 7:34 AM




Re: Invariant subspace problem solved?
Posted:
Mar 6, 2013 7:34 AM


On 02/28/2013 08:12 PM, David Bernier wrote: > On 02/28/2013 07:56 PM, David Bernier wrote: [...]
>> I was reading on problems considered "modulo a compact >> operator K". >> >> If T is a bounded operator on a separable, infinite >> dimensional Hilbert space H, >> >> can one show that for some compact operator K >> on H, T+K has a nontrivial invariant >> subspace? > [...] > > Ok. I think we can find a finiterank K such that > T+K has some nonzero eigenvector, i.e. > one can construct K such that for some v in H, > > T+K maps v to a scalar multiple of v. [...]
Alexey I. Popov and Adi Tcaciuc have an arxiv preprint implying that on a separable infinitedimensional Hilbert space, any operator T can be perturbed by a rankone operator K such that T + K has an invariant subspace of infinite dimension and codimension.
They prove more than that.
Cf. the abstract here:
http://arxiv.org/abs/1208.5831
David Bernier  dracut:/# lvm vgcfgrestore File descriptor 9 (/.console_lock) leaked on lvm invocation. Parent PID 993: sh Please specify a *single* volume group to restore.



