can someone help me with proving the following.
How does one prove this$$w(T)=\sup_{\theta \in \mathbb{R}}||H_{\theta}||$$ where $H_{\theta}=\Re(e^{i\theta}T),w(T)=\sup\{|\lambda|:\lambda \in W(T)\}.$
I have no idea how to start, but I guess writing it out would lead something $$\sup_{\theta \in \mathbb{R}}||H_{\theta}||=\sup_{\theta \in \mathbb{R}}||\cos(\theta)T+i\sin(\theta)T||$$ I dont know how to proceed further...