This is an announcement for the paper "Norm optimization problem for linear operators in classical Banach spaces" by Daniel Pellegrino and Eduardo V. Teixeira. Abstract: We prove a linear operator T acting between l_p-type spaces attains its norm if, and only if, there exists a not weakly null maximizing sequence for T. For 1<p=q we show that any not weakly null maximizing sequence for a norm attaining operator T from l_p to l_q has a norm-convergent subsequence. We also prove that for any fixed x_0 in l_p, the set of operators T from l_p to l_q that attain their norm at x_0 is lineable. The same result is proven for the set of all operators that do not attain their norms. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 12 pages The source file(s), pell-teix-JFA02Fev09.tex: 35990 bytes, is(are) stored in gzipped form as 0902.0454.gz with size 10kb. The corresponding postcript file has gzipped size 91kb. Submitted from: dmpellegrino@gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0902.0454 or http://arXiv.org/abs/0902.0454 or by email in unzipped form by transmitting an empty message with subject line uget 0902.0454 or in gzipped form by using subject line get 0902.0454 to: math@arXiv.org.