This preview shows page 1. Sign up to view the full content.
Unformatted text preview: = range S * for any operator S , we see that range( T *-I ) 6 = V. Thus T *-I is not surjective, and hence not injective since V is nite dimensional. This shows that is an eigenvalue of T * . The converse (i.e. backwards direction) follows by applying the above to the eigen-value of T * , and using the fact that = and ( T * ) * = T . Date : July 30, 2009....
View Full Document
- Summer '08