Elliptic complexes over -algebras of compact operators

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• 作者：Svatopluk Krý ; sl ^{Svatopluk.Krysl@mff.cuni.cz" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 46M18 ; secondary ; 46L08 ; 46M20
• 刊名：Journal of Geometry and Physics
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：101
• 期：Complete
• 页码：27-37
• 全文大小：448 K

文摘

For a C^∗$C^{\ast }$-algebra A$A$ of compact operators and a compact manifold M$M$, we prove that the Hodge theory holds for A$A$-elliptic complexes of pseudodifferential operators acting on smooth sections of finitely generated projective A$A$-Hilbert bundles over M$M$. For these C^∗$C^{\ast }$-algebras and manifolds, we get a topological isomorphism between the cohomology groups of an A$A$-elliptic complex and the space of harmonic elements of the complex. Consequently, the cohomology groups appear to be finitely generated projective C^∗$C^{\ast }$-Hilbert modules and especially, Banach spaces. We also prove that in the category of Hilbert A$A$-modules and continuous adjointable Hilbert A$A$-module homomorphisms, the property of a complex of being self-adjoint parametrix possessing characterizes the complexes of Hodge type.