{"id":"palomar/PALOMAR-2026-08-22-000008","url":"https://github.com/adas1236/KaltonPeckPalomar/tree/6830235450adb5f7da6bc683f7ac6b1767320cc0","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-08-22-000008-v1.json","repo":"https://github.com/adas1236/KaltonPeckPalomar","tags":["math.FA","msc:46B03","msc:46B20","msc:47A53","functional-analysis","banach-spaces","symplectic-geometry"],"score":0,"title":"adas1236/KaltonPeckPalomar","trust":"high","domain":"math.FA","source":"palomar","authors":["Avik Das"],"reviews":0,"subject":"math.FA","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-08-22","reactions":{},"formalized":true,"formalizes":[{"title":"Kalton-Peck space is not isomorphic to its hyperplanes","identifier":"https://arxiv.org/abs/2608.02126","relationship":"formalizes"}]}