We say an operator 0 L(V, W) intertwines SE L(V) and T = L(W) if T0...

 

Transcribed Image Text:

We say an operator 0 L(V, W) intertwines SE L(V) and T = L(W) if T0 = 0S. (a) What would being an intertwiner mean in the special case that was invertible? (b) Fix S, T. Show that the subset of intertwiners is a subspace of L(V, W). (c) (Roman 10.12) Prove that if S, T are normal operators on finite-dimensional inner prod- uct spaces and intertwines (S, T), then also intertwines (S*, T*). We say an operator 0 L(V, W) intertwines SE L(V) and T = L(W) if T0 = 0S. (a) What would being an intertwiner mean in the special case that was invertible? (b) Fix S, T. Show that the subset of intertwiners is a subspace of L(V, W). (c) (Roman 10.12) Prove that if S, T are normal operators on finite-dimensional inner prod- uct spaces and intertwines (S, T), then also intertwines (S*, T*).