This is an announcement for the paper "Growth conditions and inverse producing extensions" by Catalin Badea and Vladimir Mueller. Abstract: We study the invertibility of Banach algebras elements in their extensions, and invertible extensions of Banach and Hilbert space operators with prescribed growth conditions for the norm of inverses. As applications, the solutions of two open problems are obtained. In the first one we give a characterization of E(T)-subscalar operators in terms of growth conditions. In the second one we show that operators satisfying a Beurling-type growth condition possess Bishop's property beta. Other applications are also given. Archive classification: Functional Analysis; Operator Algebras Remarks: 22 pages The source file(s), bm1arx.tex: 60879 bytes, is(are) stored in gzipped form as 0512321.gz with size 19kb. The corresponding postcript file has gzipped size 90kb. Submitted from: catalin.badea@math.univ-lille1.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0512321 or http://arXiv.org/abs/math.FA/0512321 or by email in unzipped form by transmitting an empty message with subject line uget 0512321 or in gzipped form by using subject line get 0512321 to: math@arXiv.org.