Approximately isometric lifting in quasidiagonal extensions |
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Authors: | XiaoChun Fang YiLe Zhao |
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Institution: | (1) Department of Mathematics, Tongji University, Shanghai, 200092, China |
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Abstract: | Let 0 → I → A → A/I → 0 be a short exact sequence of C*-algebras with A unital. Suppose that the extension 0 → I → A → A/I → 0 is quasidiagonal, then it is shown that any positive element (projection, partial isometry, unitary element, respectively)
in A/I has a lifting with the same form which commutes with some quasicentral approximate unit of I consisting of projections. Furthermore, it is shown that for any given positive number ε, two positive elements (projections,
partial isometries, unitary elements, respectively) in A/I, and a positive element (projection, partial isometry, unitary element, respectively) a which is a lifting of , there is a positive element (projection, partial isometry, unitary element, respectively) b in A which is a lifting of such that ∥a−b∥ < . As an application, it is shown that for any positive numbers ε and in U(A/I)
0
, there exists u in U(A)0 which is a lifting of such that cel(u) < cel .
This work was supported by National Natural Science Foundation of China (Grant No. 10771161) |
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Keywords: | commutativity lifting quasidiagonal extension |
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