本质正规性与齐次子模的可分解性
Essential normality and the decomposability of homogeneous submodules
摘要：
建立了有限秩d-移位Hilbert模的一类新的齐次子模的本质正规性。其主要思想是一个基本可分解性的概念，它决定了一个任意的子模何时可以分解为基本正规子模之和。我们证明了每一个基本可分解的子模是基本正常的，并利用凸几何的思想，我们介绍的方法，建立一个子模是基本可分解的。证明了有限秩d-移位希尔伯特模的许多齐次子模都具有这个性质。我们证明了许多其他作者考虑的子模基本上是可分解的，并建立了一个大的新类的齐次子模的基本可分解性。我们的结果支持了Arveson的猜想：有限秩d-移位Hilbert模的每个齐次子模本质正规。
英文摘要：
We establish the essential normality of a large new class of homogeneous submodules of the finite rank d-shift Hilbert module. The main idea is a notion of essential decomposability that determines when an arbitrary submodule can be decomposed into the sum of essentially normal submodules. We prove that every essentially decomposable submodule is essentially normal, and using ideas from convex geometry, we introduce methods for establishing that a submodule is essentially decomposable. It turns out that many homogeneous submodules of the finite rank d-shift Hilbert module have this property. We prove that many of the submodules considered by other authors are essentially decomposable, and in addition establish the essential decomposability of a large new class of homogeneous submodules. Our results support Arveson's conjecture that every homogeneous submodule of the finite rank d-shift Hilbert module is essentially normal.
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