[Author] Oleg Reinov [Title] O-frames for operators in Banach spaces [AMS Subj-class] 46B28 Spaces of operators; tensor products; approximation properties [Abstract] A new notion of an O-frame for an operator is introduced. For the operators in separable spaces, it is shown that a operator has an O-frame iff it has the BAP iff it can be factored through a Banach space with a basis. Applications are given. [Comments] LaTeX, Russian, 11 pp. [Contact e-mail] orein51@mail.ru