Multiplication operators on the Bergman space via analytic continuation

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dc.creatorDouglas, Ronald G.
dc.creatorSun, Shunhua
dc.creatorZheng, Dechao
dc.date2009-01-23
dc.date.accessioned2026-07-07T12:34:22Z
dc.date.available2026-07-07T12:34:22Z
dc.descriptionIn this paper, using the group-like property of local inverses of a finite Blaschke product $ϕ$, we will show that the largest $C^*$-algebra in the commutant of the multiplication operator $M_ϕ$ by $ϕ$ on the Bergman space is finite dimensional, and its dimension equals the number of connected components of the Riemann surface of $ϕ^{-1}\circϕ$ over the unit disk. If the order of the Blaschke product $ϕ$ is less than or equal to eight, then every $C^*$-algebra contained in the commutant of $M_ϕ$ is abelian and hence the number of minimal reducing subspaces of $M_ϕ$ equals the number of connected components of the Riemann surface of $ϕ^{-1}\circϕ$ over the unit disk.
dc.identifierhttps://arxiv.org/abs/0901.3787
dc.identifierhttp://arxiv.org/abs/0901.3787
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217409
dc.subjectFunctional Analysis
dc.subject47B35, 46E20
dc.titleMultiplication operators on the Bergman space via analytic continuation
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