paper

C*-algebraic Gauss-Lucas Theorem and C*-algebraic Sendov's Conjecture

arXiv:2203.06916 · doi:10.26117/2079-6641-2026-54-1-56-63

Abstract

Using a result of Robertson \textit{[Proc. Edinburgh Math. Soc. (2), 1976]}, we introduce a notion of differentiation of maps on certain classes of unital commutative C*-algebras. We then derive C*-algebraic Gauss-Lucas theorem and formulate C*-algebraic Sendov's conjecture. We verify C*-algebraic Sendov's conjecture for polynomials of degree 2.

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