Open Access
June, 2004 Approximation and symbolic calculus for Toeplitz algebras on the Bergman space
Daniel Suárez
Rev. Mat. Iberoamericana 20(2): 563-610 (June, 2004).


If $f\in L^\infty(\mathbb{D})$ let $T_f$ be the Toeplitz operator on the Bergman space $L^2_a$ of the unit disk $\mathbb{D}$. For a $C^\ast$-algebra $A\subset L^\infty(\mathbb{D})$ let $\mathfrak{T}(A)$ denote the closed operator algebra generated by $\{ T_f : f\in A \}$. We characterize its commutator ideal $\comm(A)$ and the quotient $\mathfrak{T}(A)/ \mathfrak{C}(A)$ for a wide class of algebras $A$. Also, for $n\geq 0$ integer, we define the $n$-Berezin transform $B_nS$ of a bounded operator $S$, and prove that if $f\in L^\infty(\mathbb{D})$ and $f_n = B_n T_f$ then $T_{f_n} \rightarrow T_f$.


Download Citation

Daniel Suárez. "Approximation and symbolic calculus for Toeplitz algebras on the Bergman space." Rev. Mat. Iberoamericana 20 (2) 563 - 610, June, 2004.


Published: June, 2004
First available in Project Euclid: 17 June 2004

zbMATH: 1057.32005
MathSciNet: MR2073132

Primary: ‎32A36‎
Secondary: 47B35

Keywords: Bergman space , commutator ideal and abelianization , Toeplitz operator

Rights: Copyright © 2004 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.20 • No. 2 • June, 2004
Back to Top