The commutant of an operator with bounded conjugation orbits and $C_0$-contractions.

Mohamed Zarrabi (1)

1 IMB - Institut de Mathématiques de Bordeaux

Let $A$ be an invertible bounded linear operator on a complex Banach space, $\{A\}'$ the commutant of $A$ and $B_A$ the set of all operators $T$ such that $\sup_{n\geq 0} \|A^nTA^{-n}\|<+\infty$. Equality $\{A\}'= B_A$ was studied by many authors for differents classes of operators. In this paper we investigate a local version of this equality and the case where $A$ is a $C_0$-contraction.

Mots clés: Operators; commutant; bounded conjugation orbit; $C_0$--contraction

Domaines: Analyse fonctionnelle [math.FA]; Algèbres d'opérateurs [math.OA]

Mohamed Zarrabi. The commutant of an operator with bounded conjugation orbits and $C_0$-contractions.. Extracta Mathematicae, 2012, 27 (2), pp.175-185. ⟨hal-00959070⟩