Stability for Some Operator Classes by Aluthge Transform

Gilles Cassier (1) , Jérôme Verliat (1)

1 EDPA - Équations aux dérivées partielles, analyse

Our purpose is to investigate various stability properties of the Aluthge transform of an operator acting on a Hilbert space H. We begin with the stability of partial isometries, with some examples in Hardy spaces. Then we obtain some interesting relations about minimum polynomial, iterated kernels and iterated ranges between an operator and its Aluthge transform. And we finish with an analysis of stability of C0; and C1; operator classes.

Mots clés: Aluthge transform; isometry; generalized Toeplitz operator; iterated kernel; iterated range; minimum function of an operator.; minimum function of an operator

Domaines: Analyse fonctionnelle [math.FA]

Gilles Cassier, Jérôme Verliat. Stability for Some Operator Classes by Aluthge Transform. Operator Theory Live, Theta, 2010, pp.51-67. ⟨hal-00864094⟩