This is an announcement for the paper "The spectral mapping theorem" by Narinder S Claire. Abstract: We prove the Spectral Mapping Theorem for the Helffer-Sj\"ostrand functional calculus for linear operators on Banach spaces with real spectra and consequently give a new proof for the Spectral Mapping Theorem for self-adjoint operators on Hilbert spaces. Archive classification: math.SP math.FA Mathematics Subject Classification: 47A60 Remarks: latex 12 pages The source file(s), integral.eps: 33099 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1001.0232 or http://arXiv.org/abs/1001.0232 or by email in unzipped form by transmitting an empty message with subject line uget 1001.0232 or in gzipped form by using subject line get 1001.0232 to: math@arXiv.org.