O-frames for operators in Banach spaces

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 Pełczyński. 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 a...

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Published in:arXiv.org 2014-08
Main Author: Reinov, Oleg
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Banach spaces
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description 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 Pełczyński. 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 Pełczyński.
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subjects Banach spaces
Operators
title O-frames for operators in Banach spaces
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