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

Abstract

The Kalton-Peck $Z_2$ space is the derived space obtained from the scale of ${\ell }_p$ spaces by complex interpolation at $1/2$. If we denote by by $Z_2^{real}$ the derived space obtained from the scale of ${\ell }_p$ spaces by real interpolation at $(1/2,1/2)$, we show that $Z_2$ is the complexification of $Z_2^{real}$. We also show that $Z_2^{real}$ shares the most important properties of $Z_2$: it is isomorphic to its dual, it is singular and contains no complemented copies of ${\ell }_2$.

arXiv comment10pp