This is an announcement for the paper "Remarks on Naimark's duality" by Wojciech Czaja. Abstract: We present an extension of Naimark's duality principle which states that complete systems in a Hilbert space are projections of $\omega$-linearly independent systems of elements of an ambient Hilbert space. This result is presented in the context of other known extensions of Naimark's theorem. Archive classification: Functional Analysis Mathematics Subject Classification: 42C40 The source file(s), rnd_4.tex: 15949 bytes, is(are) stored in gzipped form as 0410348.gz with size 5kb. The corresponding postcript file has gzipped size 36kb. Submitted from: czaja@math.uni.wroc.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0410348 or http://arXiv.org/abs/math.FA/0410348 or by email in unzipped form by transmitting an empty message with subject line uget 0410348 or in gzipped form by using subject line get 0410348 to: math@arXiv.org.