Compact operators that commute with a contraction
Language
en
Article de revue
This item was published in
Integral Equations and Operator Theory. 2009-12-10, vol. 65, n° 4, p. 543-550
Springer Verlag
English Abstract
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 ...Read more >
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 $\lim_{n\to \infty} T^nf(T) =0$.Read less <
English Keywords
compact operators
essentially unitary
commutant
ANR Project
Dynamique des opérateurs - ANR-07-BLAN-0249
Origin
Hal imported