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Consistency of a counterexample to Naimark's problem.

Abstract：

:We construct a C*-algebra that has only one irreducible representation up to unitary equivalence but is not isomorphic to the algebra of compact operators on any Hilbert space. This answers an old question of Naimark. Our construction uses a combinatorial statement called the diamond principle, which is known to be consistent with but not provable from the standard axioms of set theory (assuming that these axioms are consistent). We prove that the statement "there exists a counterexample to Naimark's problem which is generated by aleph (1) elements" is undecidable in standard set theory.

journal_name

Proc Natl Acad Sci U S A

journal_title

Proceedings of the National Academy of Sciences of the United States of America

authors

Akemann C,Weaver N

doi

10.1073/pnas.0401489101

keywords:

subject

Has Abstract

pub_date

2004-05-18 00:00:00

pages

7522-5

issue

20

eissn

0027-8424

issn

1091-6490

pii

0401489101

journal_volume

101

pub_type

杂志文章

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