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, 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
-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
-algebras, Duke Math. J. 33 (1966), 413-416. MR 33 #1750. MR 0193530 (33:1750)
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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