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Interpolation Theory and Geometry of Banach Spaces

Abstract

The theory of interpolation of Banach spaces arose from the need to prove the continuity of certain operators defined on $L_p$ spaces, being generalized to the study of operators in Banach spaces in general. An interpolation scale between $X_0$ and $X_1$ can be seen as a deformation of the space $X_0$ to the space $X_1$, and the intermediate spaces have properties that, in general, merge the properties of $X_0$ and $X_1$. Furthermore, it is common for interpolation methods to generate a twisted sum of the interpolation space through the derivation process. This project aims to study applications of the theory of interpolation to the geometry of Banach spaces, through the study of derived spaces, commutator estimates, and interpolation and derivation of concrete spaces. (AU)

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