2026/08/03 by A. Das, V. Ferenczi, Ch. Rosendal
Mathematics · #math.FA #msc:46B03 #msc:46B20 #msc:47A53
12 pages
arxiv created 2026/08/03 · arxiv updated 2026/08/04
Let Z2 denote the real Kalton-Peck space. No hyperplane of Z2 admits a complex structure, and Z2 is even in the sense of Ferenczi-Galego. Therefore, Z2 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 Z2, the Castillo-González-Pino Fredholm theorem in Z2, 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.