Dynamics of Properties of Toeplitz Operators with Radial Symbols

Part of the Operator Theory: Advances and Applications book series (OT, volume 185)


Given a smooth defining symbol a=a(z), the family of Toeplitz operators \( T_a = \left\{ {T_a^{\left( h \right)} } \right\} \), where h∈(0, 1), was considered in the previous chapter under the Berezin quantization procedure. For a fixed h the Toeplitz operator T a (h) acts on the weighted Bergman space \( \mathcal{A}_h^2 \left( \mathbb{D} \right) \), where the parameter h characterizes the weight (10.1.5) on \( \mathcal{A}_h^2 \left( \mathbb{D} \right) \). In the sequel we will consider another form of presentation of the weighted Bergman spaces, see (10.1.1), the space \( \mathcal{A}_\lambda ^2 \left( \mathbb{D} \right) \) which is parameterized by λ∈(−1, +∞) being connected with h∈(0, 1) by the rule \( \lambda + 2 = \frac{1} {h} \), see Section 10.1.


Toeplitz Operator Bergman Space Compactness Property Weighted Bergman Space Bounded Symbol 
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© Birkhäuser Verlag AG 2008

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