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arXiv · 2204.01703

Symplectic forms on Banach spaces

Jesús M. F. Castillo·Wilson Cuellar·Manuel González Ortiz·Raúl Pino
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Abstract

We extend and generalize the result of Kalton and Swanson ($Z_2$ is a symplectic Banach space with no Lagrangian subspace) by showing that all higher order Rochgberg spaces $\mathfrak R^{(n)}$ are symplectic Banach spaces with no Lagrangian subspaces. The nontrivial symplectic structure on even spaces is the one induced by the natural duality; while the nontrivial symplectic structure on odd spaces requires perturbation with a complex structure. We will also study symplectic structures on general Banach spaces and, motivated by the unexpected appearance of complex structures, we introduce and study almost symplectic structures.

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Jesús M. F. Castillo, Wilson Cuellar, Manuel González Ortiz, Raúl Pino. 2022-04-01. Symplectic forms on Banach spaces. https://arxiv.org/abs/2204.01703

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