Spaceability and algebrability in the theory of domains of existence in Banach spaces

Algebrability of some subsets of the disk algebra

“…It is clear that algebrability implies lineability. The concept of algebrability has been also defined by Gurariy and first pointed out in [6], but then has rapidly been investigated by other authors, for example [3,4,6,7,8]. In [8] Aron and Seoane-Sep úlveda showed that there exists an infinitely generated algebra in the set of everywhere surjective functions on C. In [7], Aron, Pérez-García and Seoane-Sep úlveda showed that the set of continuous functions whose Fourier series expansion diverges is algebrable.…”