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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Stable isomorphism of hereditary $C^ *$-subalgebras and stable equivalence of open projections
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by Shuang Zhang PDF
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 ${(A \otimes K)^{**}}$.
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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