Reducing subspaces for analytic multipliers of the Bergman space

Details Reducing subspaces for analytic multipliers of the Bergman space Reducing subspaces for analytic multipliers of the Bergman space

2011-10-21

arxiv.org/abs/1110.4920v1

Mathematics

Functional Analysis

Scientific paper

We answer affirmatively the problem left open in \cite{DSZ,GSZZ} and prove that for a finite Blaschke product $\phi$, the minimal reducing subspaces of the Bergman space multiplier $M_\phi$ are pairwise orthogonal and their number is equal to the number $q$ of connected components of the Riemann surface of $\phi^{-1}\circ \phi$. In particular, the double commutant $\{M_\phi,M_\phi^\ast\}'$ is abelian of dimension $q$. An analytic/arithmetic description of the minimal reducing subspaces of $M_\phi$ is also provided, along with a list of all possible cases in degree of $\phi$ equal to eight.

Affiliated with

Also associated with

No associations

Rating

Reducing subspaces for analytic multipliers of the Bergman space does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Reducing subspaces for analytic multipliers of the Bergman space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Reducing subspaces for analytic multipliers of the Bergman space will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-564087