Proper asymptotic unitary equivalence in KK-theory and projection lifting from the corona algebra |
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Authors: | Hyun Ho Lee |
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Institution: | Department of Mathematics, Seoul National University, Seoul, South Korea 151-747 |
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Abstract: | In this paper we generalize the notion of essential codimension of Brown, Douglas, and Fillmore using KK-theory and prove a result which asserts that there is a unitary of the form ‘identity + compact’ which gives the unitary equivalence of two projections if the ‘essential codimension’ of two projections vanishes for certain C∗-algebras employing the proper asymptotic unitary equivalence of KK-theory found by M. Dadarlat and S. Eilers. We also apply our result to study the projections in the corona algebra of C(X)⊗B where X is 0,1], (−∞,∞), 0,∞), and 0,1]/{0,1}. |
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Keywords: | KK-theory Proper asymptotic unitary equivalence Absorbing representation Essential codimension |
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