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The normed space numerical index of $ C\sp*$-algebras


Author: Tadashi Huruya
Journal: Proc. Amer. Math. Soc. 63 (1977), 289-290
MSC: Primary 46L05
DOI: https://doi.org/10.1090/S0002-9939-1977-0438138-2
MathSciNet review: 0438138
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Abstract: Given a complex $ {C^\ast}$-algebra X, we prove that the normed space numerical index $ n(X)$ of X is 1 or $ \tfrac{1}{2}$ according as X is commutative or not commutative.

References [Enhancements On Off] (What's this?)

  • [1] F. F. Bonsall and J. Duncan, Numerical ranges. II, London Math. Soc. Lecture Note Series, 10, Cambridge Univ. Press, London, 1973. MR 0442682 (56:1063)
  • [2] M. J. Crabb, J. Duncan and C. M. McGregor, Characterizations of commutativity for $ {C^\ast}$-algebras, Glasgow Math. J. 15 (1974), 172-175. MR 50 #14252. MR 0361807 (50:14252)
  • [3] B. Russo and H. A. Dye, A note on unitary operators in $ {C^\ast}$-algebras, Duke Math. J. 33 (1966), 413-416. MR 33 #1750. MR 0193530 (33:1750)

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DOI: https://doi.org/10.1090/S0002-9939-1977-0438138-2
Keywords: $ {C^\ast}$-algebra, numerical index, numerical radius, numerical range
Article copyright: © Copyright 1977 American Mathematical Society

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