FOM: logical status of invariant subspace problem
Matthew Frank
mfrank at math.uchicago.edu
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).
--Matt
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