This is an announcement for the paper "Isomorphic Schauder decompositions in certain Banach spaces" by Vitalii Marchenko. Abstract: We extend a theorem of Kato on similarity for sequences of projections in Hilbert spaces to the case of isomorphic Schauder decompositions in certain Banach spaces. To this end we use $\ell_{\Psi}$-Hilbertian and $\infty$-Hilbertian Schauder decompositions instead of orthogonal Schauder decompositions, generalize the concept of an orthogonal Schauder decomposition in a Hilbert space and introduce the class of spaces with Schauder-Orlicz decompositions. Furthermore, we generalize the notions of type, cotype, infratype and $M$-cotype of a Banach space and study the properties of unconditional Schauder decompositions in spaces possessing certain geometric structure. Archive classification: math.FA Mathematics Subject Classification: 47A46, 46B15, 47B40 Remarks: 35 pages Submitted from: vitalii.marchenko@karazin.ua The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1309.6552 or http://arXiv.org/abs/1309.6552