Commutative algebras of Toeplitz operators on the Reinhardt domains

Raul Quiroga-Barranco, Nikolai Vasilevski

Resultado de la investigación: Contribución a una revistaArtículo

15 Citas (Scopus)

Resumen

Let D be a bounded logarithmically convex complete Reinhardt domain in Cn 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 |z1|, |z 2|,... , |zn|) is commutative. We show that the natural action of the n-dimensional torus Tdbl;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.

Idioma originalInglés
Páginas (desde-hasta)67-98
Número de páginas32
PublicaciónIntegral Equations and Operator Theory
Volumen59
N.º1
DOI
EstadoPublicada - 1 sep 2007

Huella dactilar

Reinhardt Domain
Toeplitz Operator
Commutative Algebra
Foliation
Leaves
Bergman Metric
Totally Geodesic
Equidistant
Tangent Bundle
Unit ball
Unit Disk
C*-algebra
n-dimensional
Torus
Transverse
Complement
Subset

Citar esto

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Commutative algebras of Toeplitz operators on the Reinhardt domains. / Quiroga-Barranco, Raul; Vasilevski, Nikolai.

En: Integral Equations and Operator Theory, Vol. 59, N.º 1, 01.09.2007, p. 67-98.

Resultado de la investigación: Contribución a una revistaArtículo

TY - JOUR

T1 - Commutative algebras of Toeplitz operators on the Reinhardt domains

AU - Quiroga-Barranco, Raul

AU - Vasilevski, Nikolai

PY - 2007/9/1

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N2 - Let D be a bounded logarithmically convex complete Reinhardt domain in Cn 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 |z1|, |z 2|,... , |zn|) is commutative. We show that the natural action of the n-dimensional torus Tdbl;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.

AB - Let D be a bounded logarithmically convex complete Reinhardt domain in Cn 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 |z1|, |z 2|,... , |zn|) is commutative. We show that the natural action of the n-dimensional torus Tdbl;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.

KW - Bergman space

KW - Commutative C -algebra

KW - Reinhardt domain

KW - Separately radial symbol

KW - Toeplitz operator

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