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Proper asymptotic unitary equivalence in \KK-theory and projection lifting from the corona algebra
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\sp*-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 where is , , , and
.Comment: 14 pages, to appear in JF
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