Invariant subspaces of arbitrary multiplicity for the shift on \(\ell^1\) (Q2718956)

Let \(T\) be a bounded linear operator on a Banach space \(X\). A subset \(C\) of \(X\) is said to be cyclic for \(T\) if the linear span of the set \(\{T^n x\mid x\in C\), \(n= 0,1,2,\dots\}\) is dense in \(X\). The minimal cardinality of a cyclic set for \(T\) is said to be the multiplicity of \(T\).NEWLINENEWLINE In the paper under review, it is shown that if \(n\) is a positive integer or \(n= \infty\), then the unilateral shift \(S\) on \(\ell^1\) has an invariant subspace \(Y\) such that \(S| Y\), the restriction of \(S\) on \(Y\), has multiplicity \(n\).