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Proceedings of the American Mathematical Society

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Numerical radius preserving operators on $ B(H)$

Author: Jor-Ting Chan
Journal: Proc. Amer. Math. Soc. 123 (1995), 1437-1439
MSC: Primary 47A12; Secondary 47B49
MathSciNet review: 1231293
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Abstract: Let H be a Hilbert space over $ \mathbb{C}$ and let $ B(H)$ denote the vector space of all bounded linear operators on H. We prove that a linear isomorphism $ T:B(H) \to B(H)$ is numerical radius-preserving if and only if it is a multiply of a $ {C^ \ast }$-isomorphism by a scalar of modulus one.

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