Abstract and Applied Analysis

Nonlinear Isometries on Schatten- p Class in Atomic Nest Algebras

Kan He and Qing Yuan

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Abstract

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, H respectively. Let 𝒞 p ( H ) Alg  𝒩 be the space of Schatten- p class operators in Alg  𝒩 . When 1 p < + and p 2 , we give a complete characterization of nonlinear surjective isometries on 𝒞 p ( H ) Alg  𝒩 . If p = 2 , we also prove that a nonlinear surjective isometry on 𝒞 2 ( H ) Alg  𝒩 is the translation of an orthogonality preserving map.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 810862, 5 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412273246

Digital Object Identifier
doi:10.1155/2014/810862

Mathematical Reviews number (MathSciNet)
MR3186980

Zentralblatt MATH identifier
07023124

Citation

He, Kan; Yuan, Qing. Nonlinear Isometries on Schatten- $p$ Class in Atomic Nest Algebras. Abstr. Appl. Anal. 2014 (2014), Article ID 810862, 5 pages. doi:10.1155/2014/810862. https://projecteuclid.org/euclid.aaa/1412273246


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