论文标题
紧凑型歧管上希尔伯特捆绑包上的椭圆算子的图像是关闭的
Images of elliptic operators on Hilbert bundles on compact manifolds are closed
论文作者
论文摘要
我们证明，相对于自然的希尔伯特拓扑结构，椭圆形算子在紧凑型歧管上平滑的希尔伯特纤维束上的图像封闭。我们考虑操作员的张量产品，相对于紧凑型操作员的C*代数的作用是不变的，并将张量产品的图像与原始操作员的图像进行比较。这为这些结构建立了霍奇理论的基础。
We prove that the image of an elliptic operator on a smooth separable Hilbert fibre bundle on compact manifolds is closed with respect to the natural pre-Hilbert topology. We consider a tensor product of the operator, which is invariant with respect to an action of the C*-algebra of compact operators, and compare the image of this tensor product with the image of the original operator. This establishes a ground for the Hodge theory for these structures.
