This is an announcement for the paper "Eigenvalues of completely nuclear maps and completely bounded projection constants" by Hun Hee Lee. Abstract: We investigate the distribution of eigenvalues of completely nuclear maps on an operator space. We prove that eigenvalues of completely nuclear maps are square-summable in general and summable if the underlying operator space is Hilbertian and homogeneous. Conversely, if eigenvalues are summable for all completely nuclear maps, then every finite dimensional subspace of the underlying operator space is uniformly completely complemented. As an application we consider an estimate of completely bounded projection constants of $n$-dimensional operator spaces. Archive classification: Functional Analysis; Operator Algebras Remarks: 10 pages The source file(s), EigenComNuclear.tex: 27465 bytes, is(are) stored in gzipped form as 0502335.gz with size 9kb. The corresponding postcript file has gzipped size 55kb. Submitted from: hunmada@hanmail.net The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0502335 or http://arXiv.org/abs/math.FA/0502335 or by email in unzipped form by transmitting an empty message with subject line uget 0502335 or in gzipped form by using subject line get 0502335 to: math@arXiv.org.