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arXiv · 2204.00672

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

Jesús M. F. Castillo·Yolanda Moreno Salguero
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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 $\ell_2$.

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Jesús M. F. Castillo, Yolanda Moreno Salguero. 2022-04-01. The Kalton-Peck space is the complexification of the real Kalton-Peck space. https://arxiv.org/abs/2204.00672

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