k-Hyponormality of multivariable weighted shifts

We characterize joint k-hyponormality for 2-variable weighted shifts. Using this characterization we construct a family of examples which establishes and illustrates the gap between k-hyponormality and (k + 1)-hyponormality for each k 1. As a consequence, we obtain an abstract solution to the Lifting Problem for Commuting Subnormals. © 2005 Elsevier Inc. All rights reserved