The Kalton-Peck space is the complexification of the real Kalton-Peck space

Abstract

The Kalton-Peck Z2 space is the derived space obtained from the scale of ℓp spaces by complex interpolation at 1/2. If we denote by Z2real the derived space obtained from the scale of ℓp spaces by real interpolation at (1/2,1/2), we show that Z2 is the complexification of Z2real. We also show that Z2real shares the most important properties of Z2: it is isomorphic to its dual, it is singular and contains no complemented copies of ℓ2.