C*-algebraic Gauss-Lucas Theorem and C*-algebraic Sendov's Conjecture
Operator Algebras
2026-04-03 v1 Complex Variables
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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Cite
@article{arxiv.2203.06916,
title = {C*-algebraic Gauss-Lucas Theorem and C*-algebraic Sendov's Conjecture},
author = {K. Mahesh Krishna},
journal= {arXiv preprint arXiv:2203.06916},
year = {2026}
}
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