Unboundedness of the shift operator with respect to the Franklin system in the space \(L_ 1\) (Q1083639)

Denote by \(\{f_ n\}^{\infty}_{n=0}\) the orthonormal Franklin system defined in the interval (0,1). \textit{Z. Ciesielski} and \textit{S. Kwapien} [Commentat. Math. Spec., Vol. II, dedic. L. Orlicz, 37-42 (1979; Zbl 0433.46012)] proved that the shift operator \(T: f_ n\to f_{n+1}\) is a bounded operator in \(L_ p\) for \(1<p<\infty\). The present author proves that T is unbounded in \(L_ 1\).