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引用次数: 0
摘要
引入Hilbert C * -模上C *值半线性形式对应的b样条插值问题，研究其基本性质及其解的唯一性。我们首先研究了Hilbert C *模是自对偶的情况下的问题。传递到Hilbert W * -模的集合，我们通过刻画扩展C *值半线性形式的样条插值问题何时有解来给出我们的主要结果。最后，广泛讨论了W *代数的C *理想上Hilbert C * -模的b样条插值问题的解。
B-spline interpolation problem in Hilbert C∗-modules
We introduce the B-spline interpolation problem corresponding to a C∗-valued sesquilinear form on a Hilbert C∗-module and study its basic properties as well as the uniqueness of solution. We first study the problem in the case when the Hilbert C∗-module is self-dual. Passing to the setting of Hilbert W∗-modules, we present our main result by characterizing when the spline interpolation problem for the extended C∗-valued sesquilinear form has a solution. Finally, solutions of the B-spline interpolation problem for Hilbert C∗-modules over C∗-ideals of W∗-algebras are extensively discussed.
期刊介绍：
The Journal of Operator Theory is rigorously peer reviewed and endevours to publish significant articles in all areas of operator theory, operator algebras and closely related domains.
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