Stable isomorphism of hereditary $C^ *$-subalgebras and stable equivalence of open projections
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- Proc. Amer. Math. Soc. 105 (1989), 677-682 Request permission
Abstract:
We relate the stable isomorphism of two hereditary ${C^*}$-subalgebras to the stable equivalence of the corresponding open projections. We prove that if $A$ is completely $\sigma$-unital, then ${\operatorname {her}}(p)$ and ${\operatorname {her(}}q)$ generate the same closed ideal of $A$ iff $p \otimes 1 \sim q \otimes 1$ in ${(A \otimes K)^{**}}$ iff the central supports of $p$ and $q$ in ${A^{**}}$ are the same. If, in addition, $p \bot q$, then the above three equivalent conditions are equivalent to the condition: $p \otimes 1$ and $q \otimes 1$ are in the same path component of open projections in ${(A \otimes K)^{**}}$.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 105 (1989), 677-682
- MSC: Primary 46L05; Secondary 46M20
- DOI: https://doi.org/10.1090/S0002-9939-1989-0961418-7
- MathSciNet review: 961418