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MAPPING PRESERVING NUMERICAL RANGE OF OPERATOR PRODUCTS ON C∗-ALGEBRAS

Mohamed Mabrouk
대한수학회 (The Korean Mathematical Society)|2015.11|대한수학회보 (Bulletin of the KMS)|제52권 제6호|pp. 1963-1971

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참고문헌

키워드

numerical rangeC∗-algebraspreserving the numerical range
주제분류수학

초록

Let A and B be two unital C∗-algebras. Denote by W(a) the numerical range of an element a ∈ A. We show that the condition W(ax) = W(bx), ∀x ∈ A implies that a = b. Using this, among other results, it is proved that if Φ : A → B is a surjective map such that W(Φ (a)Φ (b)Φ (c)) = W(abc) for all a, b and c ∈ A, then Φ (1) ∈ Z(B) and the map ψ = Φ (1)2Φ is multiplicative.

Abstract

Let A and B be two unital C∗-algebras. Denote by W(a) the numerical range of an element a ∈ A. We show that the condition W(ax) = W(bx), ∀x ∈ A implies that a = b. Using this, among other results, it is proved that if Φ : A → B is a surjective map such that W(Φ (a)Φ (b)Φ (c)) = W(abc) for all a, b and c ∈ A, then Φ (1) ∈ Z(B) and the map ψ = Φ (1)2Φ is multiplicative.

참고문헌 (16)

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