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

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 Z...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2022-11, Vol.515 (1), p.126374, Article 126374
Main Authors: Castillo, Jesús M.F., Moreno, Yolanda
Format: Article
Language:English
Subjects:
CKMR interpolation method
Complex interpolation
Complexification of a Banach space
Kalton-Peck space
Real interpolation
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Summary: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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2022.126374