Strongly elliptic operators and exponentiation of operator Lie algebras
DOI:
https://doi.org/10.7146/math.scand.a-126020Abstract
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.
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