FOM: logical status of invariant subspace problem

Matthew Frank mfrank at
Tue Feb 6 15:22:49 EST 2001

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).


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