The double commutant property for composition operators

1. Miguel Lacruz
2. Fernando León Saavedra
3. Srdjan Petrovic
4. Luis Rodríguez Piazza

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DOI: 10.1007/S13348-019-00244-7 DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Collectanea mathematica

Resumen

We investigate the double commutant property for a composition operator �� , induced on the Hardy space �2(�) by a linear fractional self-map � of the unit disk �. Our main result is that this property always holds, except when � is a hyperbolic automorphism or a parabolic automorphism. Further, we show that, in both of the exceptional cases, {��}′′ is the closure of the algebra generated by �� and �−1�, either in the weak operator topology, if � is a hyperbolic automorphism, or surprisingly, in the uniform operator topology, if � is a parabolic automorphism. Finally, for each type of a linear fractional mapping, we settle the question when any of the algebras involved are equal.

Fuente de los datos: Dialnet