On commutativity of C*-algebras
Glasgow mathematical journal, Tome 29 (1987) no. 1, pp. 93-97
Voir la notice de l'article provenant de la source Cambridge University Press
Two numerical characterizations of commutativity for C*-algebra (acting on the Hilbert space H) were given in [1]; one used the norms of self-adjoint operators in (Theorem 2), and the other the numerical index of (Theorem 3). In both cases the proofs were based on the result of Kaplansky which states that if the only nilpotent operator in is 0, then is commutative ([2] 2.12.21, p. 68). Of course the converse also holds.
Lin, C.-S. On commutativity of C*-algebras. Glasgow mathematical journal, Tome 29 (1987) no. 1, pp. 93-97. doi: 10.1017/S0017089500006704
@article{10_1017_S0017089500006704,
author = {Lin, C.-S.},
title = {On commutativity of {C*-algebras}},
journal = {Glasgow mathematical journal},
pages = {93--97},
year = {1987},
volume = {29},
number = {1},
doi = {10.1017/S0017089500006704},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500006704/}
}
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[4] 4.Sz-Nagy, B. and Foias, C., Harmonic analysis of operators on Hilbert Space, (Akadémiai Kiadó, Budapest, 1970). Google Scholar
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