This is an announcement for the paper "The UMD constants of the summation operators" by J\"org Wenzel. Abstract: The UMD property of a Banach space is one of the most useful properties when one thinks about possible applications. This is in particular due to the boundedness of the vector-valued Hilbert transform for functions with values in such a space. Looking at operators instead of at spaces, it is easy to check that the summation operator does not have the UMD property. The actual asymptotic behavior however of the UMD constants computed with martingales of length n is unknown. We explain, why it would be important to know this behavior, rephrase the problem of finding these UMD constants and give some evidence of how they behave asymptotically. Archive classification: Functional Analysis Mathematics Subject Classification: 46B07 (Primary); 46B03, 46B09, 47B10 (Secondary) Remarks: 22 pages The source file(s), umd_sumop.arxiv.tex: 64167 bytes, is(are) stored in gzipped form as 0407481.gz with size 18kb. The corresponding postcript file has gzipped size 85kb. Submitted from: wenzel@minet.uni-jena.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0407481 or http://arXiv.org/abs/math.FA/0407481 or by email in unzipped form by transmitting an empty message with subject line uget 0407481 or in gzipped form by using subject line get 0407481 to: math@arXiv.org.