## Positive Toeplitz operators on weighted Bergman spaces of bounded symmetric domains.(English)Zbl 0676.47016

Let $$\Omega$$ be a bounded symmetric domain in $${\mathbb{C}}^ n$$ with Bergman kernel K(z,w) normalized by the condition $$K(z,0)=K(0,w)=1$$. Let also $$T_{\mu}$$ be a Toeplitz operator with measure $$\mu$$ as symbol, defined by $(T_{\mu}f)(z)=\int_{\Omega}K_{\lambda}(z,w)f(w)d\mu (w).$ Here $$K_{\lambda}(z,w)=[K(z,w)]^{1-\lambda}$$, and $$\mu$$ be a finite complex Borel measure on $$\Omega$$. In the case $$\mu$$ positive the author obtains the necessary and sufficient conditions for boundedness, compactness and membership in Schatten classes $${\mathcal S}_ p$$ of the operator $$T_{\mu}$$.
Reviewer: N.K.Karapetianc

### MSC:

 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators 47B10 Linear operators belonging to operator ideals (nuclear, $$p$$-summing, in the Schatten-von Neumann classes, etc.)