Game Theory and the Geometry of Banach Spaces

PI将探索和应用逻辑、集合论和组合方法来研究Banach空间的几何。我们将考虑p次方可积函数空间的补子空间的同构分类，特别是那些包含在一些良子空间中的函数。我们将研究这些空间中的有界线性算子在具有更简单和更好结构的空间中分解的充要条件。研究者还将研究具有一定渐近结构的空间中的算子。我们将研究无条件基收缩的可分Banach空间的子空间和商的刻画，以及无条件序列的子序列。Banach空间理论是关于向量空间的，其中有一个非常自然的距离概念。这些空间在许多领域都很重要，包括量子力学中的数学模型。对Banach空间几何的理解在数学和工程的许多领域一直并将继续有用。特别是，逻辑、集合论和组合方法的使用将提供关于Banach空间几何结构的丰富信息。

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.