March 22, 2004
V. Lomonosov
Title: A simple proof of Burnside's Theorem on matrix algebras
Burnside's very well known and very useful theorem states that the only irreducible algebra of linear transformations on a vector space of finite dimension greater than 1 over an algebraically closed field is the algebra of all linear transformations on the space. We give a simple proof of the Burnside's Theorem. We also give an extension of Burnside's Theorem for Banach spaces, which implies general results on invariant subspaces of linear operators.