Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-23T15:16:37.407Z Has data issue: false hasContentIssue false
  • English
  • Français

Derived Ring Isomorphisms of Von Neumann Algebras

Published online by Cambridge University Press:  20 November 2018

C. Robert Miers
C. Robert Miers*
Affiliation:
University of Victoria, Victoria, British Columbia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let M be an associative *-algebra with complex scalar field. M may be turned into a Lie algebra by defining multiplication by [A, B] = AB - BA. A Lie *-subalgebra L of M is a *-linear subspace of M such that if A, B ∈ L then [A,B] ∈ L. A Lie *-isomorphism ϕ between Lie *-subalgebras L1 and L2 of *-algebras M and N is a one-one, *-linear map of L1 onto L2 such that ϕ[A, B] = [ϕ(A), ϕ(B)] for all A , B ∈ L1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 6 , December 1973 , pp. 1254 - 1268
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Dixmier, J., Les algebres d''operateurs dans l’espace Hilbertien, Cahiers Scientifiques, Fas. XXV (Gauthier-Villars, Paris, 1969).Google Scholar
2. Douglas, R. G. and Topping, D. M., Operators whose squares are zero, Rev. Roumaine Math. Pures Appl. 12 (1967), 647–652.Google Scholar
3. Herstein, I. N., Topics in ring theory (University of Chicago Press, Chicago, 1969).Google Scholar
4. Howland, R. A., Lie isomorphisms of derived rings of simple rings, Trans. Amer. Math. Soc. 145 (1969), 383–396.Google Scholar
5. Miers, C. R., Lie homomorphisms of operator algebras, Pacific J. Math. 38 (1971), 717–737.Google Scholar
6. Pearcy, C. and Topping, D., Commutators and certain Il-factors, J. Functional Analysis 3 (1969), 69–78.Google Scholar
7. Singer, I. M., Uniformly continuous representations of Lie Groups, Ann. of Math. 56 (1952), 242–247.Google Scholar
8. Sunouchi, H., Infinite Lie rings, Tôhoku Math. J. 8 (1956), 291–307.Google Scholar