This is an announcement for the paper "Strictly singular non-compact diagonal operators on HI spaces" by Spiros A. Argyros, Irene Deliyanni, and Andreas G. Tolias. Abstract: We construct a Hereditarily Indecomposable Banach space $\eqs_d$ with a Schauder basis \seq{e}{n} on which there exist strictly singular non-compact diagonal operators. Moreover, the space $\mc{L}_{\diag}(\eqs_d)$ of diagonal operators with respect to the basis \seq{e}{n} contains an isomorphic copy of $\ell_{\infty}(\N)$. \end{abstract} Archive classification: math.FA Mathematics Subject Classification: 46B28, 46B20, 46B03 The source file(s), diagonal_adt_1.tex: 147103 bytes, is(are) stored in gzipped form as 0807.2388.gz with size 39kb. The corresponding postcript file has gzipped size 213kb. Submitted from: sargyros@math.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.2388 or http://arXiv.org/abs/0807.2388 or by email in unzipped form by transmitting an empty message with subject line uget 0807.2388 or in gzipped form by using subject line get 0807.2388 to: math@arXiv.org.