Let be a complex Hilbert space; denote by Alg and the atomic nest algebra associated with the atomic nest on and the space of Schatten- class operators on, respectively. Let be the space of Schatten- class operators in Alg . When and , we give a complete characterization of nonlinear surjective isometries on . If , we also prove that a nonlinear surjective isometry on is the translation of an orthogonality preserving map.
"Nonlinear Isometries on Schatten- Class in Atomic Nest Algebras." Abstr. Appl. Anal. 2014 1 - 5, 2014. https://doi.org/10.1155/2014/810862