Nonlinear isometries on Schatten-\(p\) class in atomic nest algebras
Summary: Let \(H\) be a complex Hilbert space; denote by \(\operatorname{Alg} \mathcal N\) and \(\mathcal C_p(H)\) the atomic nest algebra associated with the atomic nest \(\mathcal N\) on \(H\) and the space of Schatten-\(p\) class operators on, \(H\) respectively. Let \(\mathcal C_p(H)\cap\operatorname{Alg} \mathcal N\) be the space of Schatten-\(p\) class operators in \(\operatorname{Alg} \mathcal N\). When \(1\leq p<+\infty\) and \(p\neq2\), we give a complete characterization of nonlinear surjective isometries on \(\mathcal C_p(H)\cap\operatorname{Alg} \mathcal N\). If \(p=2\), we also prove that a nonlinear surjective isometry on \(\mathcal C_2(H)\cap\operatorname{Alg} \mathcal N\) is the translation of an orthogonality preserving map.
scientific article; zbMATH DE number 7023124
scientific article