Strongly elliptic operators and exponentiation of operator Lie algebras - Cabral, Rodrigo A. H. M. (MATHEMATICA SCANDINAVICA, 2021)
An intriguing feature which is often present in theorems regarding the exponentiation of Lie algebras of unbounded linear operators on Banach spaces is the assumption of hypotheses on the Laplacian operator associated with a basis of the operator Lie algebra. The main objective of this work is to show that one can substitute the Laplacian by an arbitrary operator in the enveloping algebra and still obtain exponentiation, as long as its closure generates a strongly continuous one-parameter semigroup satisfying certain norm estimates, which are typical in the theory of strongly elliptic operators.