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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.
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참고문헌 (16)
참고문헌 신청
C. K. Li / 2001 / A survey on linear preservers of numerical ranges and radii / Taiwanese J. Math 5 (3) : 477 ~ 496
C. K. Li / 2012 / Maps preserving the joint numerical radius distance of operators / Linear Algebra Appl 437 (5) : 1194 ~ 1204
E. C. Lance / 1994 / Unitary operators on Hilbert C?-modules / Bull. London Math. Soc 4 (4) : 363 ~ 366
F. F. Bonsall / 1971 / Numerical ranges of operators on normed spaces and elements of normed algebras / Cambridge Univ. Press
H. L. Gau / 2007 / C?-isomorphisms, Jordan isomorphisms, and numerical range preserving maps / Proc. Amer. Math. Soc 135 (9) : 2907 ~ 2914
C. K. Li / 2012 / Maps preserving the joint numerical radius distance of operators / Linear Algebra Appl 437 (5) : 1194 ~ 1204
E. C. Lance / 1994 / Unitary operators on Hilbert C?-modules / Bull. London Math. Soc 4 (4) : 363 ~ 366
F. F. Bonsall / 1971 / Numerical ranges of operators on normed spaces and elements of normed algebras / Cambridge Univ. Press
H. L. Gau / 2007 / C?-isomorphisms, Jordan isomorphisms, and numerical range preserving maps / Proc. Amer. Math. Soc 135 (9) : 2907 ~ 2914
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