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Proper asymptotic unitary equivalence in KK-theory and projection lifting from the corona algebra

2014.03.24 18:43

실적년도	2011 년
논문구분	국외
총저자	Hyun Ho Lee
학술지명	J. Func. Anal.
권(Vol.)
호(No.)	260
게재년월	년 월
Impact Factor
SCI 등재	SCI
비고

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 $Csp*$-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 $C(X)otimes B$ where $X$ is $[0,1]$, $(-infty, infty)$, $[0,infty)$, and $[0,1]/{0,1}$.

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