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Article Dans Une Revue Integral Equations and Operator Theory Année : 2009

Compact operators that commute with a contraction

Karim Kellay
Mohamed Zarrabi
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Résumé

Let $T$ be a $C_0$--contraction on a separable Hilbert space. We assume that $I_H-T^*T$ is compact. For a function $f$ holomorphic in the unit disk $\DD$ and continuous on $\overline\DD$, we show that $f(T)$ is compact if and only if $f$ vanishes on $\sigma (T)\cap \TT$, where $\sigma (T)$ is the spectrum of $T$ and $\TT$ the unit circle. If $f$ is just a bounded holomorphic function on $\DD$, we prove that $f(T)$ is compact if and only if $\lim\limits_{n\to \infty} T^nf(T) =0$.

Dates et versions

hal-00957677 , version 1 (10-03-2014)

Identifiants

Citer

Karim Kellay, Mohamed Zarrabi. Compact operators that commute with a contraction. Integral Equations and Operator Theory, 2009, 65 (4), pp.543-550. ⟨10.1007/s00020-009-1724-8⟩. ⟨hal-00957677⟩

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