## Abstract and Applied Analysis

### Nonlinear Isometries on Schatten-$p$ Class in Atomic Nest Algebras

#### Abstract

Let $H$ be a complex Hilbert space; denote by Alg $\mathrm{\scr N}$ and ${\mathrm{\scr C}}_{p}(H)$ the atomic nest algebra associated with the atomic nest $\mathrm{\scr N}$ on $H$ and the space of Schatten-$p$ class operators on, $H$ respectively. Let ${\mathrm{\scr C}}_{p}(H)\cap \text{Alg\hspace\{0.17em\}}\mathrm{\scr N}$ be the space of Schatten-$p$ class operators in Alg $\mathrm{\scr N}$. When $1\le p<+\mathrm{\infty }$ and $p\ne 2$, we give a complete characterization of nonlinear surjective isometries on ${\mathrm{\scr C}}_{p}(H)\cap \text{Alg\hspace\{0.17em\}}\mathrm{\scr N}$. If $p=2$, we also prove that a nonlinear surjective isometry on ${\mathrm{\scr C}}_{2}(H)\cap \text{Alg\hspace\{0.17em\}}\mathrm{\scr N}$ 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

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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