Title of article :
Toeplitz Operators with Isotropic Invariant Symbols on the Fock Space
Author/Authors :
Hernández-Marroquín ، Mauricio Department of Mathematics - Facultad de Matemáticas - Universidad Veracruzana , Sánchez-Nungaray ، Armando Department of Mathematics - Facultad de Matemáticas - Universidad Veracruzana , Arroyo-Neri ، Jorge Luis Department of Mathematics - Facultad de Matemáticas - Universidad Veracruzana , González-Flores ، Carlos Department of Mathematics - Instituto Politécnico Nacional - Escuela Superior de Ingeniería Mecánica y Eléctrica
Abstract :
We define the so-called k-horizontal and k-cohorizontal symbols and study the C∗- algebras generated by Toeplitz operators with these symbols. We show that the C∗-algebra generated by Toeplitz operators which commute with every Toeplitz operator with k-cohorizontal symbols coincides with the C∗-algebra generated by Toeplitz operators with k-horizontal symbols. Moreover, we prove that this result also true for Toeplitz operators with symbols invariant under translations over any isotropic subspace. That is, the C∗-algebra generated by Toeplitz operators which commute with every Toeplitz operator with coisotropic invariant symbols coincides with the C∗-algebra generated by Toeplitz operators, whose symbols are invariant under translations of the corresponding isotropic subspace.
Keywords :
Toeplitz operators , Fock space , Symplectic geometry ,
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
