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Title: | The Kalton-Peck space is the complexification of the real Kalton-Peck space |
Authors: | Fernández Castillo, Jesús M. Moreno Salguero, Yolanda |
Keywords: | Espacio de Kalton-Peck;Interpolación compleja;Interpolación real;Método de interpolación CKMR;Complejización de un espacio de Banach;Kalton-Peck space;Complex interpolation;Real interpolation;CKMR interpolation method;Complexification of a Banach space |
Issue Date: | 2022 |
Publisher: | Elsevier |
Abstract: | The Kalton-Peck 𝑍₂ space is the derived space obtained from the scale of ℓ𝙽ₚ spaces by complex interpolation at 1/2. If we denote by Z_₂^(ᵣₑₐₗ) 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 Z_₂^(ᵣₑₐₗ). We also show that Z_₂^(ᵣₑₐₗ) shares the most important properties of 𝑍₂: it is isomorphic to its dual, it is singular and contains no complemented copies of ℓ₂. |
URI: | http://hdl.handle.net/10662/17283 |
ISSN: | 0022-247X |
DOI: | 10.1016/j.jmaa.2022.126374 |
Appears in Collections: | IMUEX - Artículos |
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j_jmaa_2022_126374.pdf | 338,1 kB | Adobe PDF | View/Open |
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