## 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

### Keywords:

basis set; Schauder basis