# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc:1701.332954

Arkiv for Matematik, 39, (1), 95-119, 1999.9
It is proved in Benamara-Nikolski [1] that if the spectrum σ($T$) of a contraction$T$with finite defects (rank($I−T$^{*}$T$)=rank ($I−TT$^{*})<∞) does not coincide with $$\bar D$$ , then the contraction is similar to a normal operator if and only if $$C_1 (T) = \mathop {\sup }\limits_{\lambda \in C\backslash \sigma (T)} \parallel (T - \lambda )^{ - 1} \parallel dist(\lambda ,\sigma (T))< \infty .$$
@inproceedings{stanislav1999linear,
title={Linear resolvent growth test for similarity of a weak contraction to a normal operator},
author={Stanislav Kupin},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203601027063763},
booktitle={Arkiv for Matematik},
volume={39},
number={1},
pages={95-119},
year={1999},
}

Stanislav Kupin. Linear resolvent growth test for similarity of a weak contraction to a normal operator. 1999. Vol. 39. In Arkiv for Matematik. pp.95-119. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203601027063763.