Multiplication operators on the Bergman space via analytic continuation
By Ronald G. Douglas, Shunhua Sun, Dechao Zheng. 2009
75 citations recorded by the source corpus.
Abstract In 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 ∘ ϕ 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 ∘ ϕ over the unit disk.
Subfields: Algebra and Number Theory, Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/3ccf4c88db77b0a402e46738379594e4290a0307
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In Algebra and Number Theory
In Applied Mathematics
Citations in the corpus
- Reducing subspaces for analytic multipliers of the Bergman space (2011, methodology): “The central result in [4] asserts that the operators {E1, · · · , Eq} can naturally be extended to bounded operators on the Bergman space L(2)a(D) which are linearly independent, and the double commutant algebra Aφ is linearly generated by these operators; that is, Aφ = {Mφ,M φ} = span{E1, · · · , E”