ISRAEL JOURNAL OF MATHEMATICS 102 (1997), 269-281 RANK-ONE WEAK MIXING FOR NONSINGULAR TRANSFORMATIONS BY TERRENCE ADAMS* P15 Dutchess Tpke, Poughkeepsie, New York 1~603, USA e-mail: tadams@math.unc.edu AND NATHANIEL FRIEDMAN Department of Mathematics, SUNY-Albany Albany, New York lZPZ2, USA e-mail: artmath@math.albany.edu AND CESAR S. SILVA** Department of Mathematics, Williams College Williamstown, Massachusetts 01~67, USA e-mail: csilva@williams.edu ABSTRACT We construct rank-one infinite measure preserving transformations sat- isfying each of the following dynamical properties: (1) Continuous L °° spectrum, conservative k-fold cartesian products but nonergodic cartesian square; (2) ergodic k-fold cartesian products; (3) nonconservative cartesian square. We show how to modify the construction of (1) to obtain type Ilia transformations with similar properties. * Current address: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599-3250, USA. ** Supported in part by National Science Foundation grant DMS-9214077. Received January 18/1995 and in revised form June 2, 1995 269