Some Observations Concerning Polynomial Convexity

Abstract

AbstractIn this paper we discuss a couple of observations related to polynomial convexity. More precisely, (i) We observe that the union of finitely many disjoint closed balls with centres in \(\bigcup _{\theta \in [0,\pi /2]}e^{i\theta }V\) is polynomially convex, where V is a Lagrangian subspace of \(\mathbb {C}^n\). (ii) We show that any compact subset K of \(\{(z,w)\in \mathbb {C}^2:q(w)=\overline{p(z)}\}\), where p and q are two non-constant holomorphic polynomials in one variable, is polynomially convex and \(\mathcal {P}(K)=\mathcal {C}(K)\). KeywordsPolynomial convexityClosed ballTotally realLagrangians2010 Mathematics Subject ClassificationPrimary: 32E20