Isometries of complex symmetric sequence spaces
Let E be a symmetric sequence space over the complex scalars. Then (I) Every bounded Hermitian operator on E is of the form \(T(x_ k)=(a_ k x_ k),\) where \((a_ k)\) is a real, bounded sequence; (II) Every isometry V of E onto itself is of the form \(V(x_ k)=(\lambda_ k x_{\pi(k)}),\) where \((\lambda_ k)\) are unimodular scalars and \(\pi\) is a permutation of the positive integers.
scientific article; zbMATH DE number 3855807