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arXiv · 1409.0165

O-frames for operators in Banach spaces

Oleg Reinov
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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.

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Oleg Reinov. 2014-08-30. O-frames for operators in Banach spaces. https://arxiv.org/abs/1409.0165

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