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2010 A ternary characterization of automorphisms of ${\mathbb B}({\mathscr H})$
Ali Taghavi Jelodar, Mohammad Sal Moslehian, Abolfazl Sanami
Nihonkai Math. J. 21(1): 1-9 (2010).


If ${\mathscr H}$ is a Hilbert space, $\varphi$ is a (not necessary linear) $*$-surjective mapping on ${\mathbb B}({\mathscr H})$ and $\varphi$ preserves the spectrum of operators of the form $ABA^{*}$, then $\varphi$ is either an algebra automorphism or an algebra anti-automorphism.


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Ali Taghavi Jelodar. Mohammad Sal Moslehian. Abolfazl Sanami. "A ternary characterization of automorphisms of ${\mathbb B}({\mathscr H})$." Nihonkai Math. J. 21 (1) 1 - 9, 2010.


Published: 2010
First available in Project Euclid: 8 April 2011

zbMATH: 1226.47037
MathSciNet: MR2798090

Primary: 47B49
Secondary: 46L05 , 47L30

Keywords: anti-automorphism , automorphism , Operator algebra , rank one operator , spectrum , trace functional,

Rights: Copyright © 2010 Niigata University, Department of Mathematics

Vol.21 • No. 1 • 2010
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