This is an announcement for the paper "O-frames for operators in Banach spaces" by Oleg Reinov.
Abstract: 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.
Archive classification: math.FA
Mathematics Subject Classification: 46B28
Remarks: 11 pages, was as a SPb Math. Soc. preprint, in RUSSIAN!
Submitted from: orein51@mail.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1409.0165
or