In 1996, it was published the seminal work of Rochberg “Higher order estimates in complex interpolation theory” (Rochberg, 1996). Among many other things, the paper contains a new method to construct new Banach spaces having an intriguing behaviour: they are simultaneously interpolation spaces and twisted sums of increasing complexity. The fundamental idea of Rochberg is to consider for each $z\in \mathbb{S}$ the space formed by the arrays of the truncated sequence of the Taylor coefficients of the elements of the Calderón space. What was probably unforeseen is that the Rochberg constructions would lead to a deep theory connecting Interpolation theory, Homology, Operator Theory and the Geometry of Banach spaces. This work aims to synthetically present such connections, an up-to-date account of the theory and a list of significative open problems.

1996 年，发表了 Rochberg 的开创性著作“复插值理论中的高阶估计”（Rochberg，1996）。除其他外，该论文还包含一种新方法来构建具有有趣行为的新 Banach 空间：它们同时是插值空间和复杂度不断增加的扭曲和。Rochberg 的基本思想是考虑每个$z\in \mathbb{小号}$由 Calderón 空间元素的泰勒系数的截断序列数组形成的空间。可能没有预料到的是，Rochberg 的构造将导致连接插值理论、同源论、算子理论和 Banach 空间几何的深层理论。这项工作旨在综合呈现这些联系、最新的理论说明和一系列重要的未解决问题。