[Authors] Oleg Reinov [Title] On a question of Boris Mitjagin [AMS Subj-class] 47B10 Operators belonging to operator ideals [Abstract] This is a general version of the talks at the International Conferences: 1) "On products of nuclear operators", Relations Between Banach Space Theory and Geometric Measure Theory, 08 - 12 June 2015, Mathematics Institute, University of Warwick, Coventry, United Kingdom; 2) "On a question of Boris Mitjagin", XXIV St.Petersburg Summer Meeting in Mathematical Analysis and a Summer School for Young Scientists, June 25-30, 2015, Euler International Mathematical Institute, St. Petersburg. The main result is that, generally, a product of two nuclear operators can not be factored through a Hilbert space trace-operator. [Comments] LaTeX, English, 25 pp. [Contact e-mail] orein51@mail.ru