# Journal of Operator Theory

Volume 44, Issue 2, Fall 2000 pp. 255-275.

A lifting theorem giving an isomorphism of ${\rm KK}$-products in bounded and unbounded {\rm KK}-theory**Authors**: Dan Kucerovsky

**Author institution:**University of New Brunswick at Fredericton, Department of Mathematics, P.O. Box 4400, Fredericton, N.B., E3B 5A3, Canada

**Summary:**We prove a generalization of the Kasparov technical theorem. It is known that ${\rm KK}$-theory cycles can be defined using unbounded operators ([3]), even in the equivariant case ([15]). We apply this generalized Kasparov technical theorem to a problem involving the Kasparov product of cycles defined by unbounded operators. In some earlier work ([15] and [16]) we showed that the Kasparov product can be defined directly in terms of unbounded cycles, provided that the cycles satisfy certain conditions. In this paper we show that these conditions are necessary as well as sufficient, after equivalence.

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