I am struggling with something that I think should be obvious but I'm just not seeing it.
I'm given a $C^\star$Algebra $A$ that is not $\mathbb{C}1$.
In this setting there should exist an element $a\in A$ so that $\sigma(a)$ contains at least 2 distinct elements.
This seems somehow obvious indeed but I really don't know how to construct such an element or show its existence.
Any tips are appreciated!