Approximation and symbolic calculus for Toeplitz algebras on the Bergman space
If f ∈ L∞(D) let T_f be the Toeplitz operator on the Bergman space L^2_a of the unit disk D. For a C∗-algebra A ⊂ L∞(D) let T(A) denote the closed operator algebra generated by {Tf : f ∈ A}. We characterize its commutator ideal C(A) and the quotient T(A)/C(A) for a wide class of algebras A. Also, fo...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2004 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/110173 |
| Acceso en línea: | http://hdl.handle.net/11336/110173 |
| Access Level: | acceso abierto |
| Palabra clave: | BERGMAN SPACE TOEPLITZ OPERATOR COMMUTATOR IDEAL AND ABELIANIZATION https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | If f ∈ L∞(D) let T_f be the Toeplitz operator on the Bergman space L^2_a of the unit disk D. For a C∗-algebra A ⊂ L∞(D) let T(A) denote the closed operator algebra generated by {Tf : f ∈ A}. We characterize its commutator ideal C(A) and the quotient T(A)/C(A) for a wide class of algebras A. Also, for n ≥ 0 integer, we define the n-Berezin transform B_nS of a bounded operator S, and prove that if f ∈ L∞(D) and f_n = B_nT_f then T_f_n→T_f . |
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