Exponentiation of Lie Algebras of Linear Operators on Locally Convex Spaces
arXiv:1906.07931
Abstract
Necessary and sufficient conditions for the exponentiation of finite-dimensional real Lie algebras of linear operators on complete Hausdorff locally convex spaces are obtained, focused on the equicontinuous case - in particular, necessary conditions for exponentiation to compact Lie groups are established. Applications to complete locally convex algebras, with special attention to locally C-algebras, are given. The definition of a projective analytic vector is introduced, playing an important role in some of the exponentiation theorems.
A distinction between an "analytic vector" (page 9) and a "projective analytic vector" (page 21) has been made / The Abstract has been modified (an incorrect information has been removed) / New remarks on notations (pages 13, 14) / Theorems 2.13 and 2.14 have been withdrawn / The statements of Theorems 2.16 (now Theorem 2.14) and 3.4 have been improved / Added references: [21], [42], [43]