This paper is a short survey on the numerical range of some composition operators. The first part is devoted to composition operators on the Hilbert Hardy space H2 on the unit disk. The results are due to P. Bourdon, J. Shapiro and V. Matache.
In the second part we study the numerical range of composition operators on the Hilbert space H 2 of Dirichlet series. These results are due to H. Queffélec and the author.
The third part is devoted to compactness connected with fixed points in the setting of H2 and H 2. These results are due to H. Queffélec and the author.
@article{urn:eudml:doc:41646,
title = {Numerical ranges of some composition operators.},
journal = {RACSAM},
volume = {100},
year = {2006},
pages = {127-135},
mrnumber = {MR2267404},
zbl = {1114.47029},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41646}
}
Finet, Catherine. Numerical ranges of some composition operators.. RACSAM, Tome 100 (2006) pp. 127-135. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41646/