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Let $\mathcal A$ be a unital real standard Jordan operator algebra acting on a Hilbert space $H$ of dimension at least 2. We show that every bijection $\phi$ on $\mathcal A$ satisfying $\phi(A^2\circ B)=\phi(A)^2\circ \phi(B)$ is of the form $\phi=\varepsilon\psi$ where $\psi$ is an automorphism on $\mathcal A$ and $\varepsilon \in \{-1, 1\}$. As a consequence if $\mathcal A$ is the real algebra of all self-adjoint operators on a Hilbert space $H$, then there exists a unitary or conjugate unitary operator $U$ on $H$ such that $\phi(A)=\varepsilon UAU^{*}$ for all $A\in \mathcal A$.
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참고문헌 (16)
참고문헌 신청
F. Lu / 2002 / Additivity of Jordan maps on standard operator algebras / Linear Algebra Appl 357 : 123 ~ 131
H. Hanche-Olsen / 1984 / Jordan Operator Algebras / Pitman
J. Hakeda / 1986 / Additivity of Jordan ?-maps between operator algebras / J. Math. Soc. Japan 38 (3) : 403 ~ 408
J. Hakeda / 1986 / Additivity of Jordan ?-maps on AW*-algebras / Proc. Amer. Math. Soc 96 (3) : 413 ~ 420
L. Molnar / 1999 / Some multiplicative preservers on B(H) / Linear Algebra Appl 301 (1-3) : 1 ~ 13
H. Hanche-Olsen / 1984 / Jordan Operator Algebras / Pitman
J. Hakeda / 1986 / Additivity of Jordan ?-maps between operator algebras / J. Math. Soc. Japan 38 (3) : 403 ~ 408
J. Hakeda / 1986 / Additivity of Jordan ?-maps on AW*-algebras / Proc. Amer. Math. Soc 96 (3) : 413 ~ 420
L. Molnar / 1999 / Some multiplicative preservers on B(H) / Linear Algebra Appl 301 (1-3) : 1 ~ 13
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