论文标题
与无限维矢量束和泊松矢量空间有关的微积分的方面
Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces
论文作者
论文摘要
我们证明了无限维差分计算的各种结果，这些计算将功能的不同性能和相关的运算符值功能（例如差异）相关联。结果应用于两个领域：1。在无限维矢量束的理论中，以从给定的捆绑包中构建新捆绑包，例如双束，拓扑张量产品，无限直接总和和完成（在适当的假设下）。 2。在局部凸电泊松矢量空间的理论中，以证明泊松支架的连续性以及从函数到相关的汉密尔顿矢量场的连续性。拓扑矢量空间的拓扑特性对于研究至关重要，这使双线性映射的不稳定被利用。值得注意的是，我们遇到$ k _ {\ mathbb r} $ - 空格和本地凸空间$ e $，因此$ e \ times e $是a $ k _ {\ mathbb r} $ - space。
We prove various results in infinite-dimensional differential calculus which relate differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: 1. in the theory of infinite-dimensional vector bundles, to construct new bundles from given ones, like dual bundles, topological tensor products, infinite direct sums, and completions (under suitable hypotheses). 2. in the theory of locally convex Poisson vector spaces, to prove continuity of the Poisson bracket and continuity of passage from a function to the associated Hamiltonian vector field. Topological properties of topological vector spaces are essential for the studies, which allow hypocontinuity of bilinear mappings to be exploited. Notably, we encounter $k_{\mathbb R}$-spaces and locally convex spaces $E$ such that $E\times E$ is a $k_{\mathbb R}$-space.
