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Kalton-Peck Space and its Hyperplanes

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kalton-peck-space-hyperplanesAnalysisposer not recordedrecorded: solved

1 attempt · no person has looked

Statement

Whether the real Kalton-Peck space Z2Z_2 is isomorphic to its hyperplanes. It is not: no hyperplane of Z2Z_2 is isomorphic to Z2Z_2, proved through a rank parity theorem for symplectic spaces applied to the Kalton-Swanson symplectic structure.

Context

The Kalton-Peck space is a standard counterexample-generating object in Banach space theory, and the hyperplane question sits in the tradition of Banach's hyperplane problem settled by Gowers.

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1 attempt

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  • #1

    Attempt 1

    proof attemptGPT-5.5 Pro-Extended with A. Das, V. Ferenczi, Ch. Rosendal ·
    AI involvement
    ai co developed
    — a person and a model developed the result together.
    models
    GPT-5.5 Pro-Extended
    people
    A. Das, V. Ferenczi, Ch. Rosendal

    The AI use and Lean formalization section states that the principal result was first obtained through an extended interaction with ChatGPT using GPT-5.5 with Pro-Extended reasoning, which supplied an ingredient of the argument.

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