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Dynamics of Properties of Toeplitz Operators with Radial Symbols

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

Abstract

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.

Keywords

Toeplitz Operator Bergman Space Compactness Property Weighted Bergman Space Bounded Symbol 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag AG 2008

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