We study Schauder bases for spaces of holomorphic functions in the open unit disk \(\mathbb {D}\) . Given a non-Blaschke sequence \((\lambda _n)_{n\ge 1}\) in \(\mathbb {D}\) , we show that the associated sequence of finite Blaschke products \((B_n)_{n\ge 1}\) forms a Schauder basis for \(\textrm{Hol}(\overline{\mathbb {D}})\) when this space is endowed with a norm inherited from a Banach space X satisfying a set of natural structural assumptions. This abstract framework includes, in particular, the classical Hardy spaces \(H^p\) , \(1\le p\le \infty \) , the weighted Bergman spaces \(A_\alpha ^p\) , \(1\le p\le \infty \) , \(\alpha >-1\) , and BMOA. We further prove that if the sequence \((\lambda _n)_{n\ge 1}\) is contained in a compact subset of the open unit disk, then \((B_n)_{n\ge 1}\) is a Schauder basis for \(\textrm{Hol}(\overline{\mathbb {D}})\) endowed with its natural topology. Moreover, in the case of Hardy spaces \(H^p\) , \(1<p<\infty \) , we provide a complete characterization of those sequences \((\lambda _n)_{n\ge 1}\) for which the corresponding sequence of finite Blaschke products forms a Schauder basis. Finally, we discuss related phenomena in the context of the disk algebra \(\mathcal {A}(\mathbb D)\) .
