FOM: logical status of invariant subspace problem

[Matthew Frank]

Joe Shipman recently mentioned the invariant subspace problem as a
candidate for independence from ZFC.  It may be relevant that its a 
priori logical complexity is fairly high, Pi_1^2:

Every bounded operator on a Hilbert space has an invariant subspace,
or equivalently

For every sequence of numbers representing a bounded operator A
 there is a sequence of numbers representing a projection operator P
such that PAP = AP (as infinite matrices).

--Matt