Transitive operators and a problem of Halmos Ciprian FoiasIl Bong JungEungil KoCarl Pearcy 47A15invariant subspacetransitive operator In this note we show that a (still open) problem raised by Halmos in [P.R. Halmos, \textit{Ten problems in Hilbert space}, Bull. Amer. Math. Soc. \textbf{76} (1970), 887--933] is related to the general invariant subspace problem for operators on Hilbert space (and may be equivalent to it). Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.2948 10.1512/iumj.2007.56.2948 en Indiana Univ. Math. J. 56 (2007) 119 - 134 state-of-the-art mathematics http://iumj.org/access/