Book Review
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MathSciNet review:
1568007
Full text of review:
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Book Information:
Author:
Sh\^oichir\^o Sakai
Title:
Operator algebras in dynamical systems
Additional book information:
Encyclopedia of Mathematics and its Applications, vol. 41, Cambridge University Press, Cambridge, 219 + 12 pp., US$59.50. ISBN 0-521-40096.
I. Gelfand and M. Neumark, On the imbedding of normed rings into the ring of operators in Hilbert space, Rec. Math. [Mat. Sbornik] N.S. 12(54) (1943), 197–213 (English, with Russian summary). MR 0009426
James G. Glimm, On a certain class of operator algebras, Trans. Amer. Math. Soc. 95 (1960), 318–340. MR 112057, DOI 10.1090/S0002-9947-1960-0112057-5
Irving Kaplansky, Modules over operator algebras, Amer. J. Math. 75 (1953), 839–858. MR 58137, DOI 10.2307/2372552
J. v. Neumann, Zur Algebra der Funktionaloperationen und Theorie der normalen Operatoren, Math. Ann. 102 (1930), no. 1, 370–427 (German). MR 1512583, DOI 10.1007/BF01782352
Shôichirô Sakai, On a conjecture of Kaplansky, Tohoku Math. J. (2) 12 (1960), 31–33. MR 112055, DOI 10.2748/tmj/1178244484
Shôichirô Sakai, On commutative normal $^{\ast }$-derivations, Comm. Math. Phys. 43 (1975), 39–40. MR 372631
- [GN]
- I. M. Gelfand and M. A. Neumark, On the imbedding of normed rings into the ring of operators in Hilbert space, Mat. Sb. 12 (1943), 197-213. MR 0009426 (5:147d)
- [G]
- J. G. Glimm, On a certain class of operator algebras, Trans. Amer. Math. Soc. 95 (1960), 318-340. MR 0112057 (22:2915)
- [K]
- I. Kaplansky, Modules over operator algebras, Amer. J. Math. 75 (1953), 839-853. MR 0058137 (15:327f)
- [vN]
- J. von Neumann, Zur Algebra der Funkionaloperationen und Theorie der normalen Operatoren, Math. Ann. 102 (1930), 370-427. MR 1512583
- [S1]
- S. Sakai, On a conjecture of Kaplansky, Tôhoku Math. J. 12 (1960), 31-33. MR 0112055 (22:2913)
- [S2]
- -, On commutative normal *-derivations, Comm. Math. Phys. 43 (1975), 39-40. MR 0372631 (51:8838)
Review Information:
Reviewer:
Richard V. Kadison
Journal:
Bull. Amer. Math. Soc.
28 (1993), 133-136
DOI:
https://doi.org/10.1090/S0273-0979-1993-00331-8
