Crouzeix's conjecture is proved: for any bounded operator A and any rational f, ||f(A)|| ≤ 2 sup_{W(A)} |f|.
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A solution to Crouzeix's conjecture
Crouzeix's conjecture is proved: for any bounded operator A and any rational f, ||f(A)|| ≤ 2 sup_{W(A)} |f|.