Projects and Assignments in Pure Mathematics
Operators and invariant subspaces
An invariant subspace M for a bounded linear operator (linear mapping) T on a
complex Hilbert space is a closed linear subspace such that Tx is in M whenever x is in M.
In finite dimensions, operators always have eigenvectors, and these span invariant
subspaces, but it is an old unsolved problem whether operators on infinite-dimensional spaces
have invariant subspaces. This project will investigate what is known, both for
specific operators and in general.
Books
H. Radjavi and P. Rosenthal, Invariant subspaces, 2nd edition
Pure projects homepage