Abstract
In 1955, H. Dye defined certain projections of a C*-matrix algebraby [formula] which was used to show that in the case of factors not of type I2n, the unitarygroup determines the algebraic type of that factor. We study these projectionsand we show that in M2(C), the set of such projections includes all the projections. For infinite C*-algebra A, having a system of matrix units, we haveA ≃ Mn(A). M. Leen proved that in a simple, purely infinite C*-algebra A, the *-symmetries generate u0(A). Assuming K1(A) is trivial, we revise Leen’sproof and we use the same construction to show that any unitary close to theunity can be written as a product of eleven *-symmetries, eight of such are ofthe form 1 − 2Pi, j (ω), ω ∈ u (A). In simple, unital purely infinite C*-algebrashaving trivial K1-group, we prove that all Pi, j (ω) have trivial K0-class. Consequently, we prove that every unitary of On can be written as a finite productof *-symmetries, of which a multiple of eight are conjugate as group elements.
Original language | English |
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Pages (from-to) | 144-154 |
Number of pages | 11 |
Journal | Annals of Functional Analysis |
Volume | 3 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2012 |
Keywords
- C*-algebras
- K-class
- Matrix projection
ASJC Scopus subject areas
- Analysis
- Anatomy
- Algebra and Number Theory