A Note on Complex Interpolation of Quasi-Banach Function Spaces

TL;DR

This paper extends the theory of complex interpolation of quasi-Banach function spaces by removing the separability assumption and establishing a Wolff-reiteration result with a non-separable endpoint.

Contribution

It shows that the separability condition can be omitted in the complex interpolation characterization, broadening the applicability of the theory.

Findings

Omission of the separability assumption in interpolation spaces

Establishment of a Wolff-reiteration result with a non-separable endpoint

Enhanced understanding of complex interpolation in quasi-Banach spaces

Abstract

Kalton and Mitrea characterized complex interpolation spaces of quasi-Banach function spaces as Calder\'on products if both interpolants are separable. We show that one separability assumption may be omitted and establish a Wolff-reiteration result with one non-separable endpoint space.