Game Theory and the Geometry of Banach Spaces

PI将探索和应用逻辑，集合论和组合方法到Banach空间的几何。本文将讨论p次可积函数空间的可补子空间的同构分类，特别是包含在一些好的子空间中的可补子空间。本文将研究有界线性算子从这些空间到具有更简单和更好结构的因子通过空间的充要条件。调查员还将研究运营商从空间具有一定的渐近结构。我们将研究可分Banach空间的子空间和子空间的特征，以及具有收缩无条件基和无条件序列的子空间的特征。这些空间在许多领域都具有根本的重要性，包括量子力学的数学模型。对Banach空间几何的理解一直并将继续在数学和工程的许多领域是有用的。特别是，使用逻辑，集合论和组合方法将提供丰富的信息的几何结构的Banach空间。

The PI will explore and apply logic, set-theoretic and combinatorial methods to the geometry of Banach spaces. The isomorphic classification of the complemented subspaces of the spaces of p-power integrable functions, especially those contained in some nice subspaces, will be considered. Necessary and sufficient conditions for bounded linear operators from these spaces to factor through spaces with simpler and better structures will be studied. The investigator will also study operators from spaces with certain asymptotic structures. Characterizations of subspaces and quotients of separable Banach spaces with shrinking unconditional basis and subsequences of unconditional sequences will be investigated.Banach space theory is about vector spaces in which there is a very natural notion of distance. These spaces are of fundamental importance in many areas, including mathematical models in quantum mechanics. The understanding of the geometry of Banach spaces has been and will continue to be useful in many areas of mathematics and engineering. In particular, the use of logic, set-theoretic and combinatorial methods will provide rich information about the geometric structure of Banach spaces.