대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제52권6호
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  • Pages.1963-1971
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  • 2015
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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MAPPING PRESERVING NUMERICAL RANGE OF OPERATOR PRODUCTS ON C*-ALGEBRAS

  • MABROUK, MOHAMED (Department of Mathematics College of Applied Sciences and Department of Mathematics Faculty of Sciences)
  • 투고 : 2014.09.24
  • 발행 : 2015.11.30
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초록

Let $\mathcal{A}$ and $\mathcal{B}$ be two unital $C^*$-algebras. Denote by W(a) the numerical range of an element $a{\in}\mathcal{A}$. We show that the condition W(ax) = W(bx), ${\forall}x{\in}\mathcal{A}$ implies that a = b. Using this, among other results, it is proved that if ${\phi}$ : $\mathcal{A}{\rightarrow}\mathcal{B}$ is a surjective map such that $W({\phi}(a){\phi}(b){\phi}(c))=W(abc)$ for all a, b and $c{\in}\mathcal{A}$, then ${\phi}(1){\in}Z(B)$ and the map ${\psi}={\phi}(1)^2{\phi}$ is multiplicative.

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참고문헌

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피인용 문헌

  1. Numerical radius characterizations of elements in -algebras 2018, https://doi.org/10.1080/03081087.2017.1380595