The normed space numerical index of $C^*$-algebras
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- by Tadashi Huruya PDF
- Proc. Amer. Math. Soc. 63 (1977), 289-290 Request permission
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
- F. F. Bonsall and J. Duncan, Numerical ranges. II, London Mathematical Society Lecture Note Series, No. 10, Cambridge University Press, New York-London, 1973. MR 0442682, DOI 10.1017/CBO9780511662515
- M. J. Crabb, J. Duncan, and C. M. McGregor, Characterizations of commutativity for $C^{\ast }$-algebras, Glasgow Math. J. 15 (1974), 172–175. MR 361807, DOI 10.1017/S0017089500002378
- B. Russo and H. A. Dye, A note on unitary operators in $C^{\ast }$-algebras, Duke Math. J. 33 (1966), 413–416. MR 193530, DOI 10.1215/S0012-7094-66-03346-1
Additional Information
- © Copyright 1977 American Mathematical Society
- 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