This is an announcement for the paper "On the size of certain subsets of invariant Banach sequence spaces" by Tony K. Nogueira and Daniel Pellegrino. Abstract: In this note we improve some recent results of G. Botelho and V. F\'{a}varo on invariant Banach sequence spaces. Our main result shows that, under very weak assumptions, more general versions of some subsets of invariant sequence spaces investigated by G. Botelho and V. F\'{a}varo in 2014 contain, up to the null vector, a closed infinite-dimensional subspace . Archive classification: math.FA Submitted from: pellegrino@pq.cnpq.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1504.08238 or http://arXiv.org/abs/1504.08238