Some calculations for Hilbert modules
Some calculations for Hilbert modules
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发表时间：
1993
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通讯作者：
R. Douglas;G. Misra
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作者：
R. Douglas;G. Misra
在[3]、[4]、[5]等一系列文献中，第一作者基于函数代数的Hilbert模的概念，研究了Hilbert空间上有界线性算子的一种新的研究方法。尽管人们可以用这种新语言重新表达许多单个算子结果，但它的真实的希望在于多变量情况的可能性以及算子理论与代数几何之间的联系。然而，在实现这一点之前，必须奠定基础，并制定实例。不幸的是，所有的例子，无论多么基本，都依赖于相当混乱和不平凡的计算。在这份说明中，我们记录了一些这样的计算在1986年夏天，而第二作者是支持作为一个postdoctral研究员的国家科学基金会赠款的第一。虽然我们会尝试把这些计算放在上下文中，但我们不会试图从中得出任何最终结论。本说明是关于正在进行的工作的初步报告。
In a series of papers [3], [4], [5], the first author has studied a new approach to the study of bounded linear operators on Hilbert space based on the notion of Hilbert modules for function algebras. Although one can reformulate many single operator results in this new language, it’s real promise lies in the possibilities for the case of several variables and the connections which are made between operator theory and algabric geometry. Before this can be realized, however, ground work must be laid and examples worked out. Unfortunately, all examples, no matter how elementary, depend on rather messy and nontrivial calculations. In this note we record some such calculations obtained during the summer, 1986, while the second author was supported as a postdoctral fellow on the National Science Foundation Grant of the first. Although, we will try to put these calculations in context we will not try to draw any final conclusions from them. This note is a preliminary report on work in progress.