A discrete framework for the interpolation of Banach spaces

Abstract

We develop a discrete framework for the interpolation of Banach spaces, which contains the well-known real and complex interpolation methods, but also more recent methods like the Rademacher, $\gamma$- and ${\ell }^q$-interpolation methods. Our framework is based on a sequential structure imposed on a Banach space, which allows us to deduce properties of interpolation methods from properties of sequential structures. Our framework has a formulation modelled after both the real and the complex interpolation methods. This enables us to extend various results, previously known only for either the real or the complex interpolation method, to all interpolation methods that fit into our framework. As applications, we prove an interpolation result for analytic operator families and an interpolation result for intersections.

63 pages. Published in Advances in Mathematics

References in corpus (5)

• Critical spaces for quasilinear parabolic evolution equations and applications
• Banach function spaces done right
• Rs-sectorial operators and generalized Triebel-Lizorkin spaces
• Stein interpolation for the real interpolation method
• A unified approach to compatibility theorems on invertible interpolated operators

Cited by in corpus (1)

• Stein interpolation for the real interpolation method