Nonlinear Isometries on Schatten-p Class in Atomic Nest Algebras

Let H be a complex Hilbert space; denote by Alg N and C-p (H) the atomic nest algebra associated with the atomic nest N on H and the space of Schatten-p class operators on, Hespectively. Let C-p(H) boolean AND Alg N be the space of Schatten-p class operators in Alg N. When 1 <= p < + infinity and p not equal 2, we give a complete characterization of nonlinear surjective isometries on C-p (H) boolean AND Alg N. If p = 2, we also prove that a nonlinear surjective isometry on C-2 (H) boolean AND Alg N is the translation of an orthogonality preserving map.