Nonlinear Isometries on Schatten- p Class in Atomic Nest Algebras

Abstract EN

Let H be a complex Hilbert space; denote by Alg ? and ? p ( H ) the atomic nest algebra associated with the atomic nest ? on H and the space of Schatten- p class operators on, H respectively.

Let ? p ( H ) ∩ Alg ? be the space of Schatten- p class operators in Alg ? .

When 1 ≤ p < + ∞ and p ≠ 2 , we give a complete characterization of nonlinear surjective isometries on ? p ( H ) ∩ Alg ? .

If p = 2 , we also prove that a nonlinear surjective isometry on ? 2 ( H ) ∩ Alg ? is the translation of an orthogonality preserving map.