Compact Operators that Commute with a Contraction |
| |
Authors: | K Kellay M Zarrabi |
| |
Institution: | 1. CMI LATP UMR–CNRS 6632, Université de Provence, 39, rue F. Joliot-Curie, 13453, Marseille cedex 13, France 2. IMB UMR–CNRS 5352, Université de Bordeaux, 351, cours de la Libération, 33405, Talence cedex, France
|
| |
Abstract: | Let T be a C0–contraction on a separable Hilbert space. We assume that IH − T*T is compact. For a function f holomorphic in the unit disk
\mathbbD{\mathbb{D}} and continuous on
`(\mathbbD)]\overline{{\mathbb{D}}}, we show that f(T) is compact if and only if f vanishes on
s(T)?\mathbbT\sigma(T)\cap{\mathbb{T}}, where σ(T) is the spectrum of T and
\mathbbT{\mathbb{T}} the unit circle. If f is just a bounded holomorphic function on
\mathbbD{\mathbb{D}}, we prove that f(T) is compact if and only if limn? ¥||Tnf(T)|| = 0\lim\limits_{n\rightarrow \infty}\|T^{n}f(T)\| = 0. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|