Lomonosov's invariant subspace theorem

Lomonosov's invariant subspace theorem is a mathematical theorem from functional analysis concerning the existence of invariant subspaces of a linear operator on some complex Banach space.

The theorem was proved in 1973 by the Russian–American mathematician Victor Lomonosov.

(

be the space of bounded linear operators from some space

For an operator

we call a closed subspace

an invariant subspace if

be an infinite dimensional complex Banach space,

be compact and such that

be an operator that commutes with

Then there exist an invariant subspace

of the operator