Compact operators that commute with a contraction
| dc.creator | Kellay, Karim | |
| dc.creator | Zarrabi, Mohamed | |
| dc.date | 2008-09-18 | |
| dc.date.accessioned | 2026-07-07T10:03:46Z | |
| dc.date.available | 2026-07-07T10:03:46Z | |
| dc.description | 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 $\bar\DD$, we show that $f(T)$ is compact if and only if $f$ vanishes on $σ(T)\cap \TT$, where $σ(T)$ 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 $\lim_{n\to \infty} T^nf(T) =0$. | |
| dc.description | 10p | |
| dc.identifier | https://arxiv.org/abs/0809.3184 | |
| dc.identifier | http://arxiv.org/abs/0809.3184 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169417 | |
| dc.subject | Functional Analysis | |
| dc.subject | 47B05 (Primary) 30H05 (Secondary) | |
| dc.title | Compact operators that commute with a contraction | |
| dc.type | text |