Abstract
We consider the integrability problem for Lie algebras of (generally unbounded) operators in Banach space X . In addition, a Lie group G is given acting strongly continuously on X . Smoothness is defined as a relative notion with respect to the “ basepoint action.” We consider a class of smooth perturbations of Lie algebras and establish integrability for the perturbed operator Lie algebra. We also have a structure theoretic result for the components of the Levi decomposition of the perturbed Lie algebra. We give applications to automorphic Lie actions on C ∗-algebras, and to Lie algebras of derivations. A sequel paper restricts the setting further to the case of the irrational rotation C ∗-algebras. There a classification of smooth actions is given using the general results of the present paper.
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