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On basis sets in Banach spaces. (English) Zbl 1242.46017

A set \(M\subset X\) (\(X\) a Banach space) is a basis set if every \(x\in X\) can be written \(x= \sum_k c_k e_k\) where \(e_k\in M\), \(c_k\in\mathbb{R}\) or \(\mathbb{C}\) and this is unique up to permutation. (This is not same as Schauder bases.) Four open problems are posed.

MSC:

46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
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