Year: 2026
Type: preprint
Abstract: Let $Z_2$ denote the real Kalton-Peck space. No hyperplane of $Z_2$ admits a complex structure, and $Z_2$ is even in the sense of Ferenczi-Galego. Therefore, $Z_2$ is not linearly isomorphic to its hyperplanes, solving a long-standing conjecture in Banach space theory. The argument uses the Kalton-Swanson symplectic form on $Z_2$, the Castillo-González-Pino Fredholm theorem in $Z_2$, and a special case of a mod-$2$ theorem of Li-Zhu on skew-adjoint Fredholm relations in symplectic spaces, for which a self-contained proof is included.
Source: arXiv (Cornell University)
Authors: Das, A., Ferenczi, V., Rosendal, Ch.
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7172410044