Closed-range composition operators on $\mathbb{A}^{2}$
Akeroyd, John R. ; Ghatage, Pratibha G.
Illinois J. Math., Tome 52 (2008) no. 1, p. 533-549 / Harvested from Project Euclid
For analytic self-maps φ of the unit disk, we develop a necessary and sufficient condition for the composition operator Cφ to be closed-range on the classical Bergman space $\mathbb{A}^{2}$ . This condition is relatively easy to apply. Particular attention is given to the case that φ is an inner function. Included are observations concerning angular derivatives of Blaschke products. In the case that φ is univalent, it is shown that Cφ is closed-range on $\mathbb{A}^{2}$ only if φ is an automorphism of the disk.
Publié le : 2008-05-15
Classification:  47B33,  47B38,  30D55
@article{1248355348,
     author = {Akeroyd, John R. and Ghatage, Pratibha G.},
     title = {Closed-range composition operators on $\mathbb{A}^{2}$},
     journal = {Illinois J. Math.},
     volume = {52},
     number = {1},
     year = {2008},
     pages = { 533-549},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1248355348}
}
Akeroyd, John R.; Ghatage, Pratibha G. Closed-range composition operators on $\mathbb{A}^{2}$. Illinois J. Math., Tome 52 (2008) no. 1, pp.  533-549. http://gdmltest.u-ga.fr/item/1248355348/