Exponentiation of Lie Algebras of Linear Operators on Locally Convex Spaces

Rodrigo A. H. M. Cabral

Published 2019-06-19Version 1

Necessary and sufficient conditions for the exponentiation of finite-dimensional real Lie algebras of linear operators on complete locally convex spaces are obtained, with a focus on the equicontinuous case. In particular, the exponentiation issue for compact Lie groups is completely solved. Applications to projective limits of Banach spaces and to complete locally convex algebras are given, with special attention to locally C$^*$-algebras.