ON A REDUCED CROSSED PRODUCT OF A GROUP BY A C*-ALGEBRA. THE CASES OF CONTINUOUS TRACE AND TYPE I REDUCED CROSSED PRODUCT

This paper analyzes two special cases of C* -algebras, the cases of universal crossed product and reduced crossed product of a group by a C* -algebra. In the hypothesis that the universal crossed product is a continuous trace C* -algebra or a type I C* -algebra, it is proved that the reduced crossed product is a continuous trace C* -algebra or, respectively, a type I C* -algebra. Moreover, these results can be extended in the case when the crossed products are obtained from a groupoid and a bundle of C* -algebras with a constant fiber