Vol. 71, No. 2, 1977

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Stable isomorphism and strong Morita equivalence of Cāˆ—-algebras

Lawrence Gerald Brown, Philip Palmer Green and Marc Aristide Rieffel

Vol. 71 (1977), No. 2, 349ā€“363

We show that if A and B are C-algebras which possess countable approximate identities, then A and B are stably isomorphic if and only if they are strongly Morita equivalent. By considering Breuer ideals, we show that this may fail in the absence of countable approximate identities. Finally we discuss the Picard groups of C-algebras, especially for stable algebras.

Mathematical Subject Classification 2000
Primary: 46L05
Received: 16 February 1977
Published: 1 August 1977
Lawrence Gerald Brown
Philip Palmer Green
Marc Aristide Rieffel