  These notes are formal. Here, in this abstract, not in the note, we should
say that all that is in the text was done, essentially, by Aleksander
Pe{\l}czy\'nski. BUT: Anyhow, 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. However, looking around, I'd say that,
e.g., a notion of a Banach frame (and also O-frame) was implicitely introduced
by great Aleksander Pe{\l}czy\'nski.
