The purpose of this talk is to extend a result of D. A. Henero about the existence of continuous local similarity cross sections to some operator subalgebras of L(H) which play an important role in the theory of Pseudo differential operators. In 1984 B. Gramsch introduced the notion of a ψ~*- algebra and developped a perturbation theory for these algebras using explicit rational methods in order to avoid the implicit function theorem which in general doesn't hold in this context any more.
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