Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242 ; Department of Mathematics, Iowa State University, Ames, Iowa 50011
Abstract:
We construct three different families of commuting pairs of subnormal operators, jointly hyponormal but not admitting commuting normal extensions. Each such family can be used to answer in the negative a 1988 conjecture of R. Curto, P. Muhly and J. Xia. We also obtain a sufficient condition under which joint hyponormality does imply joint subnormality.