Toeplitz operators and Toeplitz algebra with symbols of vanishing oscillation (Q2835251)

It is known to specialists in function theory that the Bergman space case and the Hardy space case are quite different. In this paper, the authors show that the index calculation for Fredholm operators in the \(C^\ast\)-algebra generated by Toeplitz operators with symbols of vanishing (mean) oscillation on the Bergman space of the unit ball can be easily and completely reduced to the classic case of Toeplitz operators with continuous symbols. In particular, it is shown that this \(C^\ast\)-algebra has uncountably many Fredholm components.