Banach空间结构和算子构成的互动作用

The Interaction Between the Structure of Banach Spaces and Operators

从Banach空间结构和算子构成的互动作用这一视角,介绍Gowers-Maurey系列成果研究深化的某些新动向.全文分为:H.I.型空间研究新成果;G-M基本定理与"平方-立方猜想";本性不可比空间与G猜想;Pisier空间相关研究和关于K群K_i(B(X))的一些猜想等5小节.

In the viewpoint of the interaction between the structure of Banach spaces and operators, this paper introduces some recent developments about a series of the Gowers and Maurey＇s results. It composes of five sections. They include some results about the study of H. I. spaces; G-M＇s Basic Theorem and the ＂square-Cubic Conjecture＂; Essentionally incomparable Banach spaces and the conjecture of M. Gonzalez; Related studies to Pisier＇s Space; And some conjectures of the K-groups Ki（B（X）） of some Banach space X.