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arXiv · 2608.02126

Kalton-Peck space is not isomorphic to its hyperplanes

A. Das·V. Ferenczi·Ch. Rosendal
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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-Gonz\'alez-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.

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A. Das, V. Ferenczi, Ch. Rosendal. 2026-08-03. Kalton-Peck space is not isomorphic to its hyperplanes. https://arxiv.org/abs/2608.02126

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