×

Differentiable structure of similarity orbits. (English) Zbl 0697.47014

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

MSC:

47A65 Structure theory of linear operators

Citations:

Zbl 0572.47001
PDFBibTeX XMLCite