adas1236/KaltonPeckPalomar
We prove the following mod-2 identity for real symplectic Banach spaces: If $(X, \omega)$ is a real symplectic Banach space, and $T \in L(X)$ satisfies: (1) $I + T^+T$ is Fredholm (2) $I + T^2$ has finite rank Then $\rank(T^2 + I) \equiv \dim \ker (I + T^+T) \pmod 2$. In the above, $T^+$ represents the symplectic adjoint. See our paper for more depth in definitions. This identity is applied to show that no hyperplane of the real Kalton-Peck space has a complex structure. We note that in our notation, a symplectic Banach space always assumes that the symplectic form \omega is a strong…
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