Algebra of endomorphisms

[losiu99]

I have encountered a statement: Every automorphism of an algebra of endomorphisms of a vector space is an inner automorphism. I tried to prove it, but so far I fail. Does anyone know where can I find a proof of this theorem (it was stated as "well-known"), or provide a sketch?
Thank you very much in advance!

[arkajad]

Perhaps Skolem-Noether theorem (http://books.google.fr/books?id=MDUy78NCjy0C&pg=PA144&lpg=PA144&dq=skolem+noether+%22vector+space%22&source=bl&ots=rgpg4knRlI&sig=6Xx2kkSQ61zZG6nKaZgDTT9Q1uM&hl=fr&ei=acGkTIjSBsK4jAfxjL3ADA&sa=X&oi=book_result&ct=result&resnum=4&ved=0CCoQ6AEwAw#v=onepage&q=skolem%20noether%20%22vector%20space%22&f=false) will be useful? Or check Semisimple Algebras (http://matematicas.uniandes.edu.co/~jarteaga/trabajo-diario/sub-riemannian/geometric-control-theory/references-add/Grupos%20de%20Lie2-texto/fulltext6.pdf) - p. 154, Corollary 2.

[losiu99]

Thank you, pdf on semisimple algebras seems to contain what I was looking for. Once again, thanks for quick and accurate help!