The curvature invariant of a Hilbert module over C[z_1,...,z_d]
The curvature invariant of a Hilbert module over C[z_1,...,z_d]
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DOI：
10.1515/crll.2000.037
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发表时间：
1998-08
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影响因子：
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通讯作者：
W. Arveson
中科院分区：
文献类型：
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作者：
W. Arveson
在多变量算子理论中引入了曲率的概念，并在d变量，d=1,2,3,....的复多项式代数上建立了梯度（收缩）Hilbert模的高斯-邦尼特-切恩定理的一个类似物在（多维）复射影空间中，计算了若干显式实例的曲率不变量、欧拉特征和度，并给出了C[z_1，…]中梯度理想结构的应用。，z_d]和自由Hilbert模H^2（C^d）的闭子模的“内序列”的存在性。
A notion of curvature is introduced in multivariable operator theory and an analogue of the Gauss-Bonnet-Chern theorem is established for graded (contractive) Hilbert modules over the complex polynomial algebra in d variables, d=1,2,3,.... The curvature invariant, Euler characteristic, and degree are computed for some explicit examples based on varieties in (multidimensional) complex projective space, and applications are given to the structure of graded ideals in C[z_1,...,z_d] and to the existence of "inner sequences" for closed submodules of the free Hilbert module H^2(C^d).