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Composition operators with a minimal commutant
| Content Provider | Semantic Scholar |
|---|---|
| Author | Lacruz, Miguel León-Saavedra, Fernando Srdjan Petrovic Rodríguez-Piazza, Luis |
| Copyright Year | 2018 |
| Abstract | Abstract Let C φ be a composition operator on the Hardy space H 2 , induced by a linear fractional self-map φ of the unit disk. We consider the question whether the commutant of C φ is minimal, in the sense that it reduces to the weak closure of the unital algebra generated by C φ . We show that this happens in exactly three cases: when φ is either a non-periodic elliptic automorphism, or a parabolic non-automorphism, or a loxodromic self-map of the unit disk. Also, we consider the case of a composition operator induced by a univalent, analytic self-map φ of the unit disk that fixes the origin and that is not necessarily a linear fractional map, but in exchange its Konigs's domain is bounded and strictly starlike with respect to the origin, and we show that the operator C φ has a minimal commutant. Furthermore, we provide two examples of univalent, analytic self-maps φ of the unit disk such that C φ is compact but it fails to have a minimal commutant. |
| Starting Page | 890 |
| Ending Page | 927 |
| Page Count | 38 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/j.aim.2018.02.012 |
| Alternate Webpage(s) | http://homepages.wmich.edu/~petrovic/research/COMIC_rev.pdf |
| Alternate Webpage(s) | https://doi.org/10.1016/j.aim.2018.02.012 |
| Volume Number | 328 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
