Submitted:
17 April 2026
Posted:
20 April 2026
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Abstract
In 1829, Cauchy derived an upper bound for every root of a complex polynomial using the maximum of the absolute values of the coefficients. In 1931, Montel derived an upper bound using the sum of the absolute values of the coefficients. We derive noncommutative versions of the Cauchy and Montel bounds.
Keywords:
Cauchy bound
; Montel bound
; Banach algebra
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