The method of alternating projections is used to examine how regularity of operators associated to the ∂¯\documentclass[12pt]{minimal}
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\begin{document}$${{\bar{\partial }}}$$\end{document}-Neumann problem percolates up the ∂¯\documentclass[12pt]{minimal}
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\begin{document}$${{\bar{\partial }}}$$\end{document}-complex. The approach revolves around operator identities—rather than estimates—that hold on any Lipschitz domain in Cn\documentclass[12pt]{minimal}
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\begin{document}$${{\mathbb {C}}}^n$$\end{document}, not necessarily bounded or pseudoconvex. We show that a geometric rate of convergence in von Neumann’s alternating projection algorithm, applied to two basic projection operators, is equivalent to ∂¯\documentclass[12pt]{minimal}
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\begin{document}$${{\bar{\partial }}}$$\end{document} having closed range. This implies that compactness of the ∂¯\documentclass[12pt]{minimal}
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\begin{document}$${{\bar{\partial }}}$$\end{document}-Neumann operator percolates up the ∂¯\documentclass[12pt]{minimal}
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\begin{document}$${{\bar{\partial }}}$$\end{document}-complex whenever ∂¯\documentclass[12pt]{minimal}
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\begin{document}$${{\bar{\partial }}}$$\end{document} has closed range at the corresponding form levels.
