Let Ω be an open simply connected proper subset of the complex plane and φ an analytic self map of Ω. If f is in the Hardy-Smirnov space defined on Ω, then the operator that takes f to f ⃘ φ is a composition operator. We show that for any Ω, analytic self maps that induce bounded Hermitian composition operators are of the form Φ(w) = aw + b where a is a real number. For ceratin Ω, we completely describe values of a and b that induce bounded Hermitian composition operators.
@article{bwmeta1.element.doi-10_1515_conop-2017-0002,
author = {Gajath Gunatillake},
title = {Hermitian composition operators on Hardy-Smirnov spaces},
journal = {Concrete Operators},
volume = {4},
year = {2017},
pages = {7-17},
zbl = {06707578},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_conop-2017-0002}
}
Gajath Gunatillake. Hermitian composition operators on Hardy-Smirnov spaces. Concrete Operators, Tome 4 (2017) pp. 7-17. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_conop-2017-0002/