Operators on Banach Spaces

数学家斯特凡·巴拿赫定义了一个数学对象，我们现在称之为巴拿赫空间。理论的巴拿赫空间延长某些工作的沃尔泰拉和希尔伯特等。Banach空间上的算子构成了物理学和工程学中许多对象的数学模型。Banach空间算子理论在数学本身中有着悠久的历史，并且与数学的其他领域，包括偏微分方程和代数拓扑学有关。这个项目的重点是在某些方面的理论，经营者的Banach空间，有相关的物理，工程和数学的各个领域。这个项目的主要目标是推广有用的结果有关算子的Hilbert空间的设置的Banach空间。例如，在何种程度上的C*-代数的扩张的结果举行的代数算子的Banach空间被认为是。由于许多关于Hilbert空间上算子的证明并没有直接推广到Banach空间上的算子，因此推广这些结果需要不同的方法。从巴拿赫空间理论的结果，特别是使用概率技术，预计是有用的。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

The mathematician Stefan Banach defined a mathematical object that we now call a Banach space. The theory of Banach spaces extended certain work of Volterra and Hilbert, among others. Operators on Banach spaces form the mathematical models for many objects in physics and engineering. Banach space operator theory has a long history within mathematics itself and is connected to other areas of mathematics, including partial differential equations and algebraic topology. The focus of this project is on certain aspects of the theory of operators on Banach spaces that have relevance for physics, engineering, and various areas of mathematics. The main goal of this project is to extend useful results concerning operators on Hilbert spaces to the setting of Banach spaces. For instance, the extent to which results about extensions of C*-algebras hold for algebras of operators on Banach spaces is considered. Since many proofs about operators on Hilbert spaces do not directly generalize to operators on Banach spaces, it is expected that extending these results requires different approaches. Results from Banach space theory, especially the use of probabilistic techniques, are expected to be useful.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.