论文标题
Banach空间上的符号形式
Symplectic forms on Banach spaces
论文作者
论文摘要
我们通过表明所有高阶Rochgberg Spaces $ \ Mathfrak r^{（n）} $ is Sympletic Banach空间，没有Lagrangian子空间，扩展并概括了Kalton和Swanson（$ Z_2 $是一个没有Lagrangian子空间的符号Banach空间）。偶数空间上的非平凡符号结构是由自然二元性引起的。而奇数空间上的非平凡符号结构需要具有复杂结构的扰动。我们还将研究一般Banach空间上的合成结构，并在复杂结构的意外出现中引起的，我们引入和研究几乎是合成结构。
We extend and generalize the result of Kalton and Swanson ($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.
