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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Test problems for operator algebras

Author: Edward A. Azoff
Journal: Trans. Amer. Math. Soc. 347 (1995), 2989-3001
MSC: Primary 46L10; Secondary 16E50, 47D25
MathSciNet review: 1321565
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Abstract: Kaplansky's test problems, originally formulated for abelian groups, concern the relationship between isomorphism and direct sums. They provide a "reality check" for purported structure theories.

The present paper answers Kaplansky's problems in operator algebraic contexts including unitary equivalence of von Neumann algebras and equivalence of representations of (non self-adjoint) matrix algebras. In particular, it is shown that matrix algebras admitting similar ampliations are themselves similar.

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Additional Information

PII: S 0002-9947(1995)1321565-4
Keywords: Ampliation, direct sum, unitary equivalence, similarity
Article copyright: © Copyright 1995 American Mathematical Society