Commutative algebras of Toeplitz operators on the Reinhardt domains

Details Commutative algebras of Toeplitz operators on the Reinhardt domains Commutative algebras of Toeplitz operators on the Reinhardt domains

2012-01-10

arxiv.org/abs/1201.2170v1

Integral Equations Operator Theory 59 (2007), no. 1, 67-98

Mathematics

Operator Algebras

Scientific paper

10.1007/s00020-007-1520-2

Let $D$ be a bounded logarithmically convex complete Reinhardt domain in $\mathbb{C}^n$ centered at the origin. Generalizing a result for the one-dimensional case of the unit disk, we prove that the $C^*$-algebra generated by Toeplitz operators with bounded measurable separately radial symbols (i.e., symbols depending only on $|z_1|$, $|z_2|$, ..., $|z_n|$) is commutative. We show that the natural action of the $n$-dimensional torus $\mathbb{T}^n$ defines (on a certain open full measure subset of $D$) a foliation which carries a transverse Riemannian structure having distinguished geometric features. Its leaves are equidistant with respect to the Bergman metric, and the orthogonal complement to the tangent bundle of such leaves is integrable to a totally geodesic foliation. Furthermore, these two foliations are proved to be Lagrangian. We specify then the obtained results for the unit ball.

Affiliated with

Also associated with

No associations

Rating

Commutative algebras of Toeplitz operators on the Reinhardt domains 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 Commutative algebras of Toeplitz operators on the Reinhardt domains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Commutative algebras of Toeplitz operators on the Reinhardt domains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-602561