Isomorphisms of UHF algebras
β Scribed by Gert K Pedersen
- Publisher
- Elsevier Science
- Year
- 1978
- Tongue
- English
- Weight
- 823 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0022-1236
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π SIMILAR VOLUMES
In this paper we characterize linear maps . between two nest algebras T(N) and T(M) which satisfy the property that .(AB&BA)=. ## (A) .(B)&.(B) .(A) for all A, B # T(N). In particular, it is shown that such isomorphisms only exist if N is similar to M or M = .
We prove that a large class of triangular UHF algebras are primitive. We use two avenues to obtain our results: a direct approach in which we explicitly construct a faithful, algebraically irreducible representation of the algebra on a separable Hilbert space, as well as an indirect, algebraic appro