English

O-frames for operators in Banach spaces

Functional Analysis 2014-09-02 v1

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.

Keywords

Cite

@article{arxiv.1409.0165,
  title  = {O-frames for operators in Banach spaces},
  author = {Oleg Reinov},
  journal= {arXiv preprint arXiv:1409.0165},
  year   = {2014}
}

Comments

11 pages, was as a SPb Math. Soc. preprint, in RUSSIAN!

R2 v1 2026-06-22T05:44:49.830Z