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<p>We show that the direct product of two Stein manifolds with the Hamiltonian density property enjoys the Hamiltonian density property as well. We investigate the relation between the Hamiltonian density property and the symplectic density property. We then establish the Hamiltonian and the symplectic density property for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((\mathbb {C}^*)^{2n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mo>∗</mo> </msup> <mo stretchy="false">)</mo> </mrow> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </msup> </math></EquationSource> </InlineEquation> and for the so-called traceless Calogero–Moser spaces. As an application we obtain a Carleman-type approximation for Hamiltonian diffeomorphisms of a real form of the traceless Calogero–Moser space.</p>

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Direct Products for the Hamiltonian Density Property

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月11日

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  • Rafael B. Andrist,
  • Gaofeng Huang

摘要

We show that the direct product of two Stein manifolds with the Hamiltonian density property enjoys the Hamiltonian density property as well. We investigate the relation between the Hamiltonian density property and the symplectic density property. We then establish the Hamiltonian and the symplectic density property for \((\mathbb {C}^*)^{2n}\) ( C ∗ ) 2 n and for the so-called traceless Calogero–Moser spaces. As an application we obtain a Carleman-type approximation for Hamiltonian diffeomorphisms of a real form of the traceless Calogero–Moser space.