This is an announcement for the paper "On $l^2$ norms of some weighted mean matrices" by Peng Gao. Abstract: We give another proof of a result of Bennett on the $l^{p}$ operator norms of some weighted mean matrices for the case $p=2$. Archive classification: math.FA Mathematics Subject Classification: 47A30 Remarks: 6 pages The source file(s), Bilinearineqarxiv.tex: 25253 bytes, is(are) stored in gzipped form as 0802.3546.gz with size 7kb. The corresponding postcript file has gzipped size 71kb. Submitted from: penggao@utsc.utoronto.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0802.3546 or http://arXiv.org/abs/0802.3546 or by email in unzipped form by transmitting an empty message with subject line uget 0802.3546 or in gzipped form by using subject line get 0802.3546 to: math@arXiv.org.