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| Stability of Rotation Relations of Three Unitaries with the Flip Action in C*-Algebras* |
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Citation： |
Zhijie WANG,Junyun HU,Jiajie HUA.Stability of Rotation Relations of Three Unitaries with the Flip Action in C*-Algebras*[J].Chinese Annals of Mathematics B,2023,44(4):577~598 |
| Page view： 1322
Net amount： 736 |
Authors： |
Zhijie WANG; Junyun HU;Jiajie HUA |
Foundation： |
This work was supported by the National Natural Science Foundation of China (Nos. 11401256,11801219, 11501249, 11871342), the Scientific Research Fund of Zhejiang Provincial Education Department (No. Y202249575) and the Zhejiang Provincial Natural Science Foundation of China (No. LQ13A010016). |
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| Abstract： |
The authors show that if Θ = (θjk) is a 3 × 3 totally irrational real skewsymmetric matrix, where θjk ∈ [0, 1) for j, k = 1, 2, 3, then for any ε > 0, there exists δ > 0 satisfying the following: For any unital C*-algebra A with the cancellation property,strict comparison and nonempty tracial state space, any four unitaries u1, u2, u3, w ∈ A such that (1) ukuj - e2πiθjk ujukk < δ, wujw-1 = u-1j, w2 = 1A for j, k = 1, 2, 3; (2)τ (aw) = 0 and τ ((ukujuk*uj* )n ) = e2πinθjk for all n ∈ N, all a ∈ C*(u1, u2, u3), j, k = 1, 2, 3 and all tracial states τ on A, where C*(u1, u2, u3) is the C*-subalgebra generated by u1, u2 and u3, there exists a 4-tuple of unitaries u1, u2, u3, w in A such that ukuj = e2πinθjk ukuj, w uj w-1 = u-1 j, w2 = 1A and k uj - ujk < ε, k w - wk < ε for j, k = 1, 2, 3. The above conclusion is also called that the rotation relations of three unitaries with the flip action is stable under the above conditions. |
Keywords： |
C*-Algebras, Stability, Rotation relation, Unitary, Flip action |
Classification： |
46L05, 46L35 |
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