We study the Helton-Howe trace and the Connes-Chern character for Toeplitz operators on weighted Bergman spaces via the idea of quantization. We prove a local formula for the large t-limit of the Connes-Chern character as the weight goes to infinity. And we show that the Helton-Howe trace of Toeplitz operators is independent of the weight t and obtain a local formula for the Helton-Howe trace for all weighted Bergman spaces. The proofs are based on an integration by parts formula and some harmonic analysis. This talk is based on joint work with Xiang Tang and Dechao Zheng.

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