What is an example of a surjective homomorphism $B(H)\to\mathbb C$, where $B(H)$ is the set of bounded linear operators on a Hilbert space $H$, and $\mathbb C$ is the complex numbers.
THIS ANSWER IS WRONG!!:
Let $v\in H$ be any non-zero vector. What can you say about the map $$\varphi\mapsto \varphi(v):B(H)\to \mathbb C?$$
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1 year ago