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We give estimates for the essential norms of a positive Toeplitz operator onthe Bergman space of a minimal bounded homogeneous domain in terms of theBerezin transform or the averaging function of the symbol. Using theseestimates, we also give necessary and sufficient conditions for the positiveToeplitz operators to be compact.

Essential norm estimates for positive Toeplitz operators on the weighted Bergman space of a minimal bounded homogeneous domain