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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1231293-7
PII: S 0002-9939(1995)1231293-7
Article copyright: © Copyright 1995 American Mathematical Society