We discuss the domain of Toeplitz operators with radial symbols in the Segal-Bargmann space: we point out and correct missleading staments in previous works, establishing the conditions under which a given Toeplitz operator ...

Let L^2-a be the Bergman space of the unit disk and T(L^2_a) be the Banach algebra generated by Toeplitz operators T_f , with f ∈ L∞. We prove that the closed bilateral ideal of T(L2a) generated by operators of the form ...

To any bounded operator S on the Bergman space La2 we associate a sequence of linear transforms Bn(S ) ∈ L∞(D), where n ≧ 0, and prove that the Toeplitz operators article image tend to S for some especial classes of operators ...

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 ...

Let L2 be the Lebesgue space of square-integrable functions on the unit circle. We show that the injectivity problem for Toeplitz operators is linked to the existence of geodesics in the Grassmann manifold of L2. We also ...