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Jointly hyponormal pairs of commuting subnormal operators need not be jointly subnormal |
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| Authors: | Raú l E Curto Jasang Yoon |
| Affiliation: | 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. |
| Keywords: | Jointly hyponormal pairs subnormal pairs $2$-variable weighted shifts |
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