The normed space numerical index of 
-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 | References | Similar Articles | Additional Information
Abstract: Given a complex 
-algebra X, we prove that the normed space numerical index 
of X is 1 or 
according as X is commutative or not commutative.
- [1] F. F. Bonsall and J. Duncan, Numerical ranges. II, Cambridge University Press, New York-London, 1973. London Mathematical Society Lecture Notes Series, No. 10. MR 0442682
- [2] M. J. Crabb, J. Duncan, and C. M. McGregor, Characterizations of commutativity for 𝐶*-algebras, Glasgow Math. J. 15 (1974), 172–175. MR 0361807, https://doi.org/10.1017/S0017089500002378
- [3] B. Russo and H. A. Dye, A note on unitary operators in 𝐶*-algebras, Duke Math. J. 33 (1966), 413–416. MR 0193530
-algebras, Glasgow Math. J. 15 (1974), 172-175. MR 50 #14252. 
-algebras, Duke Math. J. 33 (1966), 413-416. MR 33 #1750. Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L05
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1977-0438138-2
Keywords:
-algebra,
numerical index,
numerical radius,
numerical range
Article copyright:
© Copyright 1977
American Mathematical Society