This is an announcement for the paper "Hardy-Littlewood inequalities for norms of positive operators on sequence spaces" by Miguel Lacruz. Abstract: We consider estimates of Hardy and Littlewood for norms of operators on sequence spaces, and we apply a factorization result of Maurey to obtain improved estimates and simplified proofs for the special case of a positive operator. Archive classification: math.FA Mathematics Subject Classification: 47B37 Remarks: 3 pages, to appear in Lin. Alg. Appl Submitted from: lacruz@us.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1208.3246 or http://arXiv.org/abs/1208.3246