Andruchow, E.; Stojanoff, D. Differentiable structure of similarity orbits. (English) Zbl 0697.47014 J. Oper. Theory 21, No. 2, 349-366 (1989). Let H be an infinite dimensional separable complex Hilbert space. Let G(H) denote the set of all invertible operators on H. For an operator T on H the similarity orbit of T is \(S(T)=\{UTU^{-1}:\) \(U\in G(H)\}.\) In this article the authors prove that S(T) is a holomorphic submanifold of B(H) if and only if T is similar to a nice Jordan operator. This class of operators is studied in [C. Apostol, L. Fialkow, D. Herrero and D. Voiculescu, approximation of Hilbert space operators, Vol. 2, Boston (1984; Zbl 0572.47001)] where they show that T belongs to this class if and only if \(\pi_ T: G(H)\to S(T)\) defined by \(\pi_ T(U)=UTU^{-1}\) has continuous local cross sections. Reviewer: K.Seddighi Cited in 1 ReviewCited in 7 Documents MSC: 47A65 Structure theory of linear operators Keywords:similarity orbit; similar to a nice Jordan operator Citations:Zbl 0572.47001 PDFBibTeX XMLCite \textit{E. Andruchow} and \textit{D. Stojanoff}, J. Oper. Theory 21, No. 2, 349--366 (1989; Zbl 0697.47014)