In this paper, we will characterize the largest self-adjoint subalgebra Q of L∞(D) such that the semi-commutators of any two Toeplitz operators on the weighted Bergman space Ap(φ) with symbols in Q is compact, and calculate the essential spectrum and the Predholm index of Toeplitz operator on Ap(φ) with the symbol in Q.
Tao YU.
Essential Spectrum of Toeplitz Operator on the Weighted Bergman Space. Acta Mathematica Sinica, Chinese Series, 2006, 49(2): 357-362 https://doi.org/10.12386/A2006sxxb0045