Composition operators Cφ induced by a selfmap φ of some set S are operators acting on a space consisting of functions on S by composition to the right with φ, that is Cφf = f º φ. In this paper, we consider the Hilbert Hardy space H2 on the open unit disk and find exact formulas for distances ||Cφ - Cψ|| between composition operators. The selfmaps φ and ψ involved in those formulas are constant, inner, or analytic selfmaps of the unit disk fixing the origin.
@article{urn:eudml:doc:41867,
title = {Distances between composition operators.},
journal = {Extracta Mathematicae},
volume = {22},
year = {2007},
pages = {19-33},
zbl = {1173.47016},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41867}
}
Matache, Valentin. Distances between composition operators.. Extracta Mathematicae, Tome 22 (2007) pp. 19-33. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41867/