Corrigendum to: “Quantization and the resolvent algebra” [J. Funct. Anal. 277 (8) (2019) 2815–2838]

Abstract

In [3] it is claimed incorrectly that the Berezin quantization map maps surjectively to the resolvent algebra.¹ We show here that it does not. Similarly, the Berezin map defined on $C_0\left(R^{2n}\right)$ does not reach all compact operators, contrary to what is claimed in [2, II.(2.73)].² We moreover fill a gap in the proof of injectivity of the Berezin quantization map on $C_R\left(X\right)$ of [3].