This is an announcement for the paper "Amenability of algebras of approximable operators" by Ariel Blanco and Niels Groenbaek. Abstract: We give a necessary and sufficient condition for amenability of the Banach algebra of approximable operators on a Banach space. We further investigate the relationship between amenability of this algebra and factorization of operators, strengthening known results and developing new techniques to determine whether or not a given Banach space carries an amenable algebra of approximable operators. Using these techniques, we are able to show, among other things, the non-amenability of the algebra of approximable operators on Tsirelson's space. Archive classification: math.FA Mathematics Subject Classification: 46B20, 47L10 (primary), 16E40 (secondary) Remarks: 20 pages, to appear in Israel Journal of Mathematics The source file(s), OnAmenability2.tex: 82733 bytes, is(are) stored in gzipped form as 0804.1725.gz with size 25kb. The corresponding postcript file has gzipped size 148kb. Submitted from: gronbaek@math.ku.dk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.1725 or http://arXiv.org/abs/0804.1725 or by email in unzipped form by transmitting an empty message with subject line uget 0804.1725 or in gzipped form by using subject line get 0804.1725 to: math@arXiv.org.