@article {
author = {Hejazian, Shirin and Safarizadeh, Mozhdeh},
title = {Bijections on the Unit Ball of $B(H)$ Preserving $^{\ast}$-Jordan Triple Product},
journal = {Sahand Communications in Mathematical Analysis},
volume = {19},
number = {3},
pages = {125-139},
year = {2022},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2022.541050.1008},
abstract = {Let $ \mathcal{B}_1$ denote the closed unit ball of $\mathcal B(H)$, the von Neumann algebra of all bounded linear operators on a complex Hilbert space $H$ with $\dim H\geq 2$. Suppose that $\phi$ is a bijection on $ \mathcal{B}_1$ (with no linearity assumption) satisfying\begin{equation*}\phi(AB^{*}A)=\phi(A)\phi(B)^{*}\phi(A), \quad( A, B\in \mathcal{B}_1).\end{equation*}If $I$ and $\mathbb T$ denote the identity operator on $H$ and the unit circle in $\mathbb C$, respectively and if $\phi$ is continuous on $\{\lambda I: \lambda\in \mathbb T\}$, then we show that $\phi(I)$ is a unitary operator and $\phi(I)\phi$ extends to a linear or conjugate linear Jordan $^*$-automorphism on $\mathcal B(H)$. As a consequence, there is either a unitary or an antiunitary operator $U$ on $H$ such that $\phi(A)=\phi(I) UAU^*$, $(A\in {\mathcal B}_1)$ or $ \phi(A)=\phi(I) UA^*U^*$, $(A\in {\mathcal B}_1)$.},
keywords = {Hilbert space,$^*$-Jordan triple product,Effect,Preserver map},
url = {https://scma.maragheh.ac.ir/article_251967.html},
eprint = {https://scma.maragheh.ac.ir/article_251967_0adf05940d21103cf91ec358bf9d7fe6.pdf}
}