Mathematical Sciences: Geometry of Banach Spaces and Operator Spaces

9623260 W. B。约翰逊和G.皮西耶 提案人将调查的问题，在理论的Banach空间和运营商空间。需要考虑的问题包括： 算子空间和可测函数空间的局部理论， 多项式有界算子，C* 代数上的有界同态， 无穷维线性和非线性Banach空间几何。 Banach空间理论形成了研究非欧几里德几何的自然框架，而C* 代数理论是量子力学的标准框架。算子空间是Banach空间的量子化（在量子力学的意义上）。 这个新的理论已经（例如，在Junge和Pisier的工作中）对C* 代数产生了影响，并且部分工作涉及通过算子空间来处理C* 代数/算子理论中的其他经典问题。 非线性几何的Banach空间也是在一个新手阶段，但工作的Bourgain，Gorelik，约翰逊-Lindenstrauss-Schechtman，和其他人表明，这一主题是准备起飞。 有理由希望，非线性理论的Banach空间将有应用在经典的非线性分析的许多应用程序的线性理论的经典线性分析。

9623260 W. B. Johnson and G. Pisier The proposers will investigate problems in the theories of Banach spaces and operator spaces. The problems to be considered involve: local theories of operator spaces and of spaces of measurable functions, polynomially bounded operators, bounded homomorphisms on C* algebras, infinite dimensional linear and nonlinear geometry of Banach spaces. Banach space theory forms the natural framework for studying geometries which are not Euclidean, while the theory of C* algebras is the standard framework for quantum mechanics. Operator spaces are the quantization (in the sense of quantum mechanics) of Banach spaces. This very new theory has already (e.g., in work of Junge and Pisier) had an impact on C* algebras, and part of this work involves approaching other classical problems in C* algebras/operator theory through operator spaces. The nonlinear geometry of Banach spaces is also in a neophyte stage, but work of Bourgain, Gorelik, Johnson-Lindenstrauss-Schechtman, and others suggest that this subject is ready to take-off. There is reason to hope that the nonlinear theory of Banach spaces will have applications in classical nonlinear analysis comparable to the many applications of the linear theory to classical linear analysis.