Differentiability of the Evolution Map and Mackey Continuity. (arXiv:1812.08777v1 [math.FA])

We solve the differentiablity problem for the evolution map in Milnor's infinite dimensional setting. We first show that the evolution map of each $C^k$-semiregular Lie group admits a particular kind of sequentially continuity $-$ called Mackey continuity $-$ and then prove that this continuity property is strong enough to ensure differentiability of the evolution map. In particular, this drops any continuity presumptions made in this context so far. Remarkably, Mackey continuity rises directly from the regularity problem itself $-$ which makes it particular among the continuity conditions traditionally considered. As a further application of the introduced notions, we discuss the strong Trotter property in the sequentially-, and the Mackey continuous context. 查看全文>>