Abstract
Dye, [Ann. of Math. (2) 61 (1955), 73-89] proved that the discrete unitary group in a factor determines the algebraic type of the factor. Afterwards, for a large class of simple unital C*-algebras, Al-Rawashdeh, Booth and Giordano [J. Funct. Anal. 262 (2012), 4711-4730] proved that the algebras are *-isomorphic if and only if their unitary groups are isomorphic as abstract groups. In this paper, we give a counterexample in the non-simple case. Indeed, we give two C*-algebras with isomorphic unitary groups but the algebras themselves are not *-isomorphic.
Original language | English |
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Pages (from-to) | 160-163 |
Number of pages | 4 |
Journal | Advances in Operator Theory |
Volume | 1 |
Issue number | 2 |
DOIs | |
Publication status | Published - Sept 1 2016 |
Externally published | Yes |
Keywords
- *-isomorphism
- C*-algebra
- Unitary group
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory