On the existence of commutative Banach-Lie groups which do not admit continuous unitary representations
We prove that every locally quasi-convex Schwartz group satisfies the Glicksberg theorem for weakly compact sets.
We revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the fixed point case (known as Zung’s theorem) we give a shorter and more geometric proof, based on a Moser deformation argument. The passage to general orbits (Weinstein) is given a more conceptual interpretation: as a manifestation of Morita invariance. We also clarify the precise statements of the Linearization Theorem (there has been some confusion on this, which has propagated throughout...