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Abstract

We consider dual Toeplitz operators acting on the orthogonal complements of two kinds of Dirichlet spaces on the unit ball. We first characterize compactness for operators which are finite sums of dual Toeplitz products. Next, we give a characterization of when a finite sum of products of two dual Toeplitz operators is another dual Toeplitz operator. Our results show that there are similarities and differences between the results on two spaces. Also our results extend several known results by providing unified ways of treating them.