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By introducing a notion of smooth connection for unbounded $KK$-cycles, we show that the Kasparov product of such cycles can be defined directly, by an algebraic formula.
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D.Kucerovsky, A lifitng theorem giving an isomorphism of K K KK -products in bounded and unbounded K K KK -theory , J. Operator Theory 44 (2000), 255-275
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D.P. Blecher, A generalization of Hilbert modules , J.Funct. An. 136, 365-421 (1996)
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D.P. Blecher, A new approach to Hilbert C ∗ C^{*} -modules , Math. Ann. 307, 253-290 (1997)
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D.P.Blecher, C. le Merdy, Operator algebras and their modules , London Mathematical Society Monographs 30
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P.S. Chakraborty and V.Mathai, The geometry of determinant line bundles in noncommutative geometry , to appear in J.Noncom. Geometry
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