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Abstract and Applied Analysis
Volume 2014, Article ID 810862, 5 pages
Research Article

Nonlinear Isometries on Schatten- Class in Atomic Nest Algebras

College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi 030024, China

Received 8 November 2013; Revised 7 February 2014; Accepted 10 February 2014; Published 17 March 2014

Academic Editor: Feliz Minhós

Copyright © 2014 Kan He and Qing Yuan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.