Prove $\forall$ compact $M:\ M \subset C\quad \exists A:l_2\rightarrow l_2, \sigma(A)=M$

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Operator whose spectrum is given compact set
Can spectrum “specify” an operator?

Prove that for each nonempty $M$ - compact subset of $\mathbf{C}$ exists operator $A:l_2 \rightarrow l_2$, such that $\sigma(A) = M$, where $\sigma$ denotes spectrum.