This is an announcement for the paper "Hereditarily indecomposable Banach algebras of diagonal operators" by Spiros A. Argyros, Irene Deliyanni, and Andreas G. Tolias. Abstract: We provide a characterization of the Banach spaces $X$ with a Schauder basis $(e_n)_{n\in\mathbb{N}}$ which have the property that the dual space $X^*$ is naturally isomorphic to the space $\mathcal{L}_{diag}(X)$ of diagonal operators with respect to $(e_n)_{n\in\mathbb{N}}$ . We also construct a Hereditarily Indecomposable Banach space ${\mathfrak X}_D$ with a Schauder basis $(e_n)_{n\in\mathbb{N}}$ such that ${\mathfrak X}^*_D$ is isometric to $\mathcal{L}_{diag}({\mathfrak X}_D)$ with these Banach algebras being Hereditarily Indecomposable. Finally, we show that every $T\in \mathcal{L}_{diag}({\mathfrak X}_D)$ is of the form $T=\lambda I+K$, where $K$ is a compact operator. Archive classification: math.FA Mathematics Subject Classification: 46B28, 47L10, 46B20, 46B03. Remarks: 35 pages, submitted for publication to Israel J. Math The source file(s), HI_DIAG.tex.bak: 124849 bytes, is(are) stored in gzipped form as 0902.1646.gz with size 33kb. The corresponding postcript file has gzipped size 188kb. Submitted from: sargyros@math.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0902.1646 or http://arXiv.org/abs/0902.1646 or by email in unzipped form by transmitting an empty message with subject line uget 0902.1646 or in gzipped form by using subject line get 0902.1646 to: math@arXiv.org.