Compact double differences of composition operators on the Bergman spaces over the ball

Choe et al. have recently characterized compact double differences formed by four composition operators acting on the standard weighted Bergman spaces over the disk of the complex plane. In this paper, we extend such a result to the ball setting. Our characterization is obtained under a suitable restriction on inducing maps, which is automatically satisfied in the case of the disk. We exhibit concrete examples, for the first time even for single composition operators, which shows that such a restriction is essential in the case of the ball.