Generalized shifts and basis vectors (Q1190325)

Banach sequence spaces are considered. The canonical shift operator \(S\) is defined as \(S(c_ 0,c_ 1,c_ 2,\dots)=(0,c_ 0,c_ 1,c_ 2,\dots)\). A vector \(x_ 0\) of \(L^ 1\) is a basis vector of \(S\), if \(\{S^ n x_ 0\}_{n=0}^ \infty\) is a basis of \(L^ 1\). Conditions to be basis vector are described, they are connected with behaviour of analytic functions in the disk.